remfin: deal with almost-Rabin automata
I.e., automata that could be Rabin if we add some empty Fin(x) or full Inf(y) sets. This way it does not matter when remove_fin() is called after cleanup_acceptance(). * src/twaalgos/remfin.cc: Implement that. * src/tests/remfin.test: More tests.
This commit is contained in:
Alexandre Duret-Lutz
parent
ef1bbfc659
commit
5f0b6dc36c
2 changed files with 376 additions and 37 deletions
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@ -158,7 +158,7 @@ State: 7 {3}
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[!0] 6
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[0] 4
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--END--
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/* echo 'i F ^ F p1 U p0 V G p0 p1 F V f p0' | ltl2dstar -H - - */
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/* echo 'i F ^ F p1 U p0 V G p0 p1 F V f p0' | ltl2dstar -H - - | fmt */
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HOA: v1 States: 14 properties: implicit-labels
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trans-labels no-univ-branch deterministic complete comment:
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"Union{Safra[NBA=9],Safra[NBA=2]}" acc-name: Rabin 5 Acceptance: 10
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@ -170,6 +170,42 @@ State: 6 {1 2 4 6 9} 12 11 4 6 State: 7 {1 2 4 6 9} 12 12 4 7 State:
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8 {0 2 4 6 9} 12 12 8 8 State: 9 {2 4 6 9} 12 11 1 3 State: 10 {1 2 4
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6 8} 10 12 5 8 State: 11 {1 2 4 6 8} 12 11 8 6 State: 12 {0 2 4 6 8}
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12 12 8 8 State: 13 {2 4 6 8} 10 11 2 3 --END--
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/* ltlfilt -l -f '(F((p1) R (p0))) | (G(F(p0)))' | ltl2dstar -H - - |
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./autfilt --merge -H | fmt
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This one is DBA-type, however because some unused acceptance sets are
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removed before calling remfin(), that function could miss the fact
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that this was a Rabin automaton...
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*/
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HOA: v1 States: 4 Start: 0 AP: 2 "p1" "p0" acc-name: Rabin 3 Acceptance:
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6 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3)) | (Fin(4) & Inf(5)) properties:
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trans-labels explicit-labels state-acc complete deterministic --BODY--
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State: 0 {2} [!1] 0 [0&1] 2 [!0&1] 3 State: 1 {1 2} [!1] 1 [1] 2 State:
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2 {1 2 5} [!1] 1 [1] 2 State: 3 {3 5} [!1] 0 [0&1] 2 [!0&1] 3 --END--
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/*
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ltlfilt -f '(X((X(p0)) R ((!(p1)) | (X(p0)))))' -l |
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ltl2dstar --automata=streett -H --ltl2nba=spin:ltl2tgba@-s - - |
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fmt
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This Streett automaton can be seen as a Rabin-like automaton with
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two pairs. So the BA-type check should apply. During testing, it
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triggered assertions.
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*/
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HOA: v1 States: 6 properties: implicit-labels trans-labels no-univ-branch
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deterministic complete comment: "Streett{Safra[NBA=5]}" acc-name: Streett
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1 Acceptance: 2 (Fin(0)|Inf(1)) Start: 5 AP: 2 "p0" "p1" --BODY-- State:
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0 {0} 0 0 0 0 State: 1 {0} 0 2 0 2 State: 2 {1} 2 2 2 2 State: 3 {}
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3 2 1 2 State: 4 {} 3 3 1 1 State: 5 {} 4 4 4 4 --END--
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/*
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ltlfilt -l -f '(F(!((1) U (!((G(p0)) -> (p1))))))' | ltl2dstar -H - - | fmt
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This Rabin automaton was incorrectly reduced at some point.
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*/
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HOA: v1 States: 4 properties: implicit-labels trans-labels no-univ-branch
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deterministic complete stutter-insensitive comment: "Safra[NBA=3]"
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acc-name: Rabin 2 Acceptance: 4 (Fin(0)&Inf(1))|(Fin(2)&Inf(3)) Start:
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1 AP: 2 "p0" "p1" --BODY-- State: 0 {2} 2 0 2 3 State: 1 {0 2} 2 1 2 2
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State: 2 {1 2} 2 0 2 2 State: 3 {3} 2 0 2 3 --END--
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EOF
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cat >expected <<EOF
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@ -403,6 +439,102 @@ State: 14 {0}
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[!0&1] 14
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[0&1] 14
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--END--
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HOA: v1
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States: 4
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Start: 0
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AP: 2 "p1" "p0"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic
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--BODY--
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State: 0
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[!1] 0
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[0&1] 2
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[!0&1] 3
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State: 1 {0}
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[!1] 1
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[1] 2
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State: 2 {0}
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[!1] 1
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[1] 2
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State: 3 {0}
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[!1] 0
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[0&1] 2
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[!0&1] 3
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--END--
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HOA: v1
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States: 6
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Start: 5
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AP: 2 "p0" "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic
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--BODY--
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State: 0
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[!0&!1] 0
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[0&!1] 0
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[!0&1] 0
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[0&1] 0
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State: 1
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[!0&!1] 0
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[0&!1] 2
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[!0&1] 0
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[0&1] 2
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State: 2 {0}
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[!0&!1] 2
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[0&!1] 2
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[!0&1] 2
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[0&1] 2
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State: 3 {0}
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[!0&!1] 3
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[0&!1] 2
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[!0&1] 1
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[0&1] 2
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State: 4
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[!0&!1] 3
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[0&!1] 3
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[!0&1] 1
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[0&1] 1
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State: 5
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[!0&!1] 4
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[0&!1] 4
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[!0&1] 4
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[0&1] 4
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--END--
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HOA: v1
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States: 5
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Start: 1
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AP: 2 "p0" "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc
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--BODY--
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State: 0
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 3
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State: 1
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[!0&!1] 2
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[0&!1] 1
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[!0&1] 2
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[0&1] 2
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State: 2 {0}
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 2
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State: 3
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 3
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[0&1] 4
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State: 4 {0}
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[0&1] 4
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--END--
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EOF
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cat >expected-tgba <<EOF
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@ -640,6 +772,102 @@ State: 14 {0}
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[!0&1] 14
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[0&1] 14
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--END--
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HOA: v1
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States: 4
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Start: 0
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AP: 2 "p1" "p0"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic
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--BODY--
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State: 0
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[!1] 0
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[0&1] 2
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[!0&1] 3
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State: 1 {0}
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[!1] 1
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[1] 2
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State: 2 {0}
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[!1] 1
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[1] 2
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State: 3 {0}
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[!1] 0
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[0&1] 2
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[!0&1] 3
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--END--
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HOA: v1
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States: 6
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Start: 5
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AP: 2 "p0" "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic
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--BODY--
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State: 0
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[!0&!1] 0
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[0&!1] 0
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[!0&1] 0
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[0&1] 0
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State: 1
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[!0&!1] 0
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[0&!1] 2
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[!0&1] 0
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[0&1] 2
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State: 2 {0}
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[!0&!1] 2
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[0&!1] 2
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[!0&1] 2
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[0&1] 2
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State: 3 {0}
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[!0&!1] 3
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[0&!1] 2
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[!0&1] 1
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[0&1] 2
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State: 4
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[!0&!1] 3
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[0&!1] 3
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[!0&1] 1
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[0&1] 1
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State: 5
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[!0&!1] 4
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[0&!1] 4
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[!0&1] 4
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[0&1] 4
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--END--
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HOA: v1
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States: 5
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Start: 1
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AP: 2 "p0" "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc
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--BODY--
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State: 0
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 3
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State: 1
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[!0&!1] 2
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[0&!1] 1
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[!0&1] 2
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[0&1] 2
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State: 2 {0}
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 2
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State: 3
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[!0&!1] 2
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[0&!1] 0
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[!0&1] 2
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[0&1] 3
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[0&1] 4
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State: 4 {0}
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[0&1] 4
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--END--
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EOF
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run 0 $autfilt -H --remove-fin test1 > output
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@ -51,7 +51,8 @@ namespace spot
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is_scc_ba_type(const const_twa_graph_ptr& aut,
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const std::vector<unsigned>& states,
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std::vector<bool>& final,
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acc_cond::mark_t inf,
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acc_cond::mark_t inf_pairs,
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acc_cond::mark_t inf_alone,
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acc_cond::mark_t sets)
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{
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// Consider the SCC as one large cycle and check its
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@ -61,8 +62,8 @@ namespace spot
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// Let f=[F₁,F₂,...] and i=[I₁,I₂,...] be bitvectors where bit
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// Fᵢ (resp. Iᵢ) indicates that Fᵢ (resp. Iᵢ) has been visited
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// in the SCC.
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acc_cond::mark_t f = (sets << 1) & inf;
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acc_cond::mark_t i = sets & inf;
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acc_cond::mark_t f = (sets << 1) & inf_pairs;
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acc_cond::mark_t i = sets & inf_pairs;
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// If we have i&!f = [0,0,...] that means that the cycle formed
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// by the entire SCC is not accepting. However that does not
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// necessarily imply that all cycles in the SCC are also
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@ -70,6 +71,7 @@ namespace spot
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// accepting, but which becomes non-accepting when extended with
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// more states.
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i -= f;
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i |= (inf_alone & sets);
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if (!i)
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{
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// Check whether the SCC is accepting. We do that by simply
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@ -85,9 +87,9 @@ namespace spot
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// procedure, because empty() will call to_tgba() wich will
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// call remove_fin()...
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sccaut->prop_state_based_acc(false);
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// If SCCAUT is empty, the SCC is DBA realizable (and none
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// If SCCAUT is empty, the SCC is BA-type (and none
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// of its states are final). If SCCAUT is nonempty, the SCC
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// is not DBA realizable.
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// is not BA type.
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return sccaut->is_empty();
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}
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// The bits remaining sets in i corresponds to I₁s that have
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@ -120,7 +122,7 @@ namespace spot
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if (si.is_rejecting_scc(scc)) // this includes trivial SCCs
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continue;
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if (!is_scc_ba_type(aut, si.states_of(scc),
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final, inf, si.acc(scc)))
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final, inf_pairs, 0U, si.acc(scc)))
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return false;
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}
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}
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@ -145,13 +147,14 @@ namespace spot
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// Büchi-typeness of the SCC, but the resulting automaton should
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// be correct nonetheless.
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static twa_graph_ptr
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ra_to_ba(const const_twa_graph_ptr& aut)
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ra_to_ba(const const_twa_graph_ptr& aut,
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acc_cond::mark_t inf_pairs,
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acc_cond::mark_t inf_alone,
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acc_cond::mark_t fin_alone)
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{
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assert(aut->has_state_based_acc());
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assert(aut->acc().is_rabin() > 0);
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scc_info si(aut);
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// For state-based Rabin automata, we check each SCC for
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// BA-typeness. If an SCC is BA-type, its final states are stored
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// in BA_FINAL_STATES.
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@ -159,11 +162,13 @@ namespace spot
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bool ba_type = false;
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std::vector<bool> ba_final_states;
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#ifdef DEBUG
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acc_cond::mark_t fin;
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acc_cond::mark_t inf;
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std::tie(inf, fin) = aut->get_acceptance().used_inf_fin_sets();
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assert((fin << 1) == inf);
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assert(inf == (inf_pairs | inf_alone));
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assert(fin == ((inf_pairs >> 1) | fin_alone));
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#endif
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ba_final_states.resize(aut->num_states(), false);
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ba_type = true; // until proven otherwise
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unsigned scc_max = si.scc_count();
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@ -174,14 +179,36 @@ namespace spot
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scc_is_ba_type[scc] = true;
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continue;
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}
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bool scc_ba_type =
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is_scc_ba_type(aut, si.states_of(scc),
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ba_final_states, inf, si.acc(scc));
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bool scc_ba_type = false;
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auto sets = si.acc(scc);
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// If there is one fin_alone that is not in the SCC,
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// any cycle in the SCC is accepting. Mark all states
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// as final.
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if ((sets & fin_alone) != fin_alone)
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{
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for (auto s: si.states_of(scc))
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ba_final_states[s] = true;
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scc_ba_type = true;
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}
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// Conversely, if all fin_alone appear in the SCC, then it
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// cannot be accepting.
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else if (sets & fin_alone)
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{
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scc_ba_type = false;
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}
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// In the generale case (no fin_alone involved), we need
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// a dedicated check.
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else
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{
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scc_ba_type = is_scc_ba_type(aut, si.states_of(scc),
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ba_final_states,
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inf_pairs, inf_alone, si.acc(scc));
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}
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ba_type &= scc_ba_type;
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scc_is_ba_type[scc] = scc_ba_type;
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}
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#if TRACE
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#ifdef TRACE
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trace << "SCC DBA-realizibility\n";
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for (unsigned scc = 0; scc < scc_max; ++scc)
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{
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@ -197,8 +224,9 @@ namespace spot
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res->copy_ap_of(aut);
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res->prop_copy(aut, { true, false, false, true });
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res->new_states(nst);
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auto final_acc = res->set_buchi();
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res->set_buchi();
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res->set_init_state(aut->get_init_state_number());
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bool deterministic = aut->is_deterministic();
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std::vector<unsigned> state_map(aut->num_states());
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for (unsigned n = 0; n < scc_max; ++n)
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@ -211,25 +239,32 @@ namespace spot
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// be marked as accepting.
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for (auto s: states)
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{
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acc_cond::mark_t acc = 0U;
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if (ba_final_states[s])
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acc = final_acc;
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bool acc = ba_final_states[s];
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for (auto& t: aut->out(s))
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res->new_edge(s, t.dst, t.cond, acc);
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res->new_acc_edge(s, t.dst, t.cond, acc);
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}
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continue;
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}
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else
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{
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// The main copy is unaccepting
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for (auto s: states)
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for (auto& t: aut->out(s))
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res->new_edge(s, t.dst, t.cond);
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deterministic = false;
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auto rem = si.acc(n) & fin;
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if (!rem)
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// No Fin sets used in this SCC.
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continue;
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// The main copy is only accepting for inf_alone
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// and for all Inf sets that have no matching Fin
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// sets in this SCC.
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acc_cond::mark_t sccsets = si.acc(n);
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acc_cond::mark_t f = (sccsets << 1) & inf_pairs;
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acc_cond::mark_t i = sccsets & (inf_pairs | inf_alone);
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i -= f;
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for (auto s: states)
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{
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bool acc = aut->state_acc_sets(s) & i;
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for (auto& t: aut->out(s))
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res->new_acc_edge(s, t.dst, t.cond, acc);
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}
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auto rem = sccsets & ((inf_pairs >> 1) | fin_alone);
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assert(rem != 0U);
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auto sets = rem.sets();
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|
||||
unsigned ss = states.size();
|
||||
|
|
@ -245,26 +280,102 @@ namespace spot
|
|||
acc_cond::mark_t acc = aut->state_acc_sets(s);
|
||||
if (acc.has(r))
|
||||
continue;
|
||||
bool jacc = acc & inf_alone;
|
||||
bool cacc = fin_alone.has(r) || acc.has(r + 1);
|
||||
for (auto& t: aut->out(s))
|
||||
{
|
||||
if (si.scc_of(t.dst) != n)
|
||||
continue;
|
||||
auto nd = state_map[t.dst];
|
||||
res->new_acc_edge(ns, nd, t.cond, t.acc.has(r + 1));
|
||||
res->new_acc_edge(ns, nd, t.cond, cacc);
|
||||
// We need only one non-deterministic jump per
|
||||
// cycle. As an approximation, we only do
|
||||
// them on back-links.
|
||||
if (t.dst <= s)
|
||||
res->new_edge(s, nd, t.cond);
|
||||
res->new_acc_edge(s, nd, t.cond, jacc);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
res->purge_dead_states();
|
||||
res->prop_deterministic(deterministic);
|
||||
return res;
|
||||
}
|
||||
|
||||
static twa_graph_ptr
|
||||
rabin_to_buchi_maybe(const const_twa_graph_ptr& aut)
|
||||
{
|
||||
if (!aut->has_state_based_acc())
|
||||
return nullptr;
|
||||
|
||||
auto code = aut->get_acceptance();
|
||||
|
||||
if (code.is_true())
|
||||
return nullptr;
|
||||
|
||||
acc_cond::mark_t inf_pairs = 0U;
|
||||
acc_cond::mark_t inf_alone = 0U;
|
||||
acc_cond::mark_t fin_alone = 0U;
|
||||
|
||||
auto s = code.back().size;
|
||||
|
||||
// Rabin 1
|
||||
if (code.back().op == acc_cond::acc_op::And && s == 4)
|
||||
goto start_and;
|
||||
// Co-Büchi
|
||||
else if (code.back().op == acc_cond::acc_op::Fin && s == 1)
|
||||
goto start_fin;
|
||||
// Rabin >1
|
||||
else if (code.back().op != acc_cond::acc_op::Or)
|
||||
return nullptr;
|
||||
|
||||
while (s)
|
||||
{
|
||||
--s;
|
||||
if (code[s].op == acc_cond::acc_op::And)
|
||||
{
|
||||
start_and:
|
||||
auto o1 = code[--s].op;
|
||||
auto m1 = code[--s].mark;
|
||||
auto o2 = code[--s].op;
|
||||
auto m2 = code[--s].mark;
|
||||
// We expect
|
||||
// Fin({n}) & Inf({n+1})
|
||||
if (o1 != acc_cond::acc_op::Fin ||
|
||||
o2 != acc_cond::acc_op::Inf ||
|
||||
m1.count() != 1 ||
|
||||
m2.count() != 1 ||
|
||||
m2 != (m1 << 1))
|
||||
return nullptr;
|
||||
inf_pairs |= m2;
|
||||
}
|
||||
else if (code[s].op == acc_cond::acc_op::Fin)
|
||||
{
|
||||
start_fin:
|
||||
fin_alone |= code[--s].mark;
|
||||
}
|
||||
else if (code[s].op == acc_cond::acc_op::Inf)
|
||||
{
|
||||
auto m1 = code[--s].mark;
|
||||
if (m1.count() != 1)
|
||||
return nullptr;
|
||||
inf_alone |= m1;
|
||||
}
|
||||
else
|
||||
{
|
||||
return nullptr;
|
||||
}
|
||||
}
|
||||
|
||||
trace << "inf_pairs: " << inf_pairs << '\n';
|
||||
trace << "inf_alone: " << inf_alone << '\n';
|
||||
trace << "fin_alone: " << fin_alone << '\n';
|
||||
return ra_to_ba(aut, inf_pairs, inf_alone, fin_alone);
|
||||
}
|
||||
|
||||
|
||||
|
||||
// If the DNF is
|
||||
// Fin(1)&Inf(2)&Inf(4) | Fin(2)&Fin(3)&Inf(1) |
|
||||
// Inf(1)&Inf(3) | Inf(1)&Inf(2) | Fin(4)
|
||||
|
|
@ -338,19 +449,19 @@ namespace spot
|
|||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
twa_graph_ptr remove_fin(const const_twa_graph_ptr& aut)
|
||||
{
|
||||
auto maybe = streett_to_generalized_buchi_maybe(aut);
|
||||
if (maybe)
|
||||
return maybe;
|
||||
|
||||
if (!aut->acc().uses_fin_acceptance())
|
||||
return std::const_pointer_cast<twa_graph>(aut);
|
||||
|
||||
if (aut->has_state_based_acc() && aut->acc().is_rabin() > 0)
|
||||
return ra_to_ba(aut);
|
||||
if (auto maybe = streett_to_generalized_buchi_maybe(aut))
|
||||
return maybe;
|
||||
|
||||
if (auto maybe = rabin_to_buchi_maybe(aut))
|
||||
return maybe;
|
||||
|
||||
std::vector<acc_cond::acc_code> code;
|
||||
std::vector<acc_cond::mark_t> rem;
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue