remfin: implement the BA-type check
* src/twaalgos/remfin.cc: Here. * src/tests/remfin.test: Add a single test. * src/twa/acc.hh (mark_t::lowest): New function.
This commit is contained in:
Alexandre Duret-Lutz
parent
8a3a07d8a4
commit
4bef219d8f
3 changed files with 345 additions and 4 deletions
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@ -158,6 +158,18 @@ 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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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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(Fin(0)&Inf(1))|(Fin(2)&Inf(3))|(Fin(4)&Inf(5))|(Fin(6)&Inf(7))|(Fin(8)&Inf(9))
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Start: 13 AP: 2 "p1" "p0" --BODY-- State: 0 {3 4 7 9} 12 11 1 0 State:
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1 {5 6 9} 12 11 1 0 State: 2 {3 4 6 9} 10 11 2 9 State: 3 {3 4 6 9}
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12 11 1 3 State: 4 {3 4 6 9} 12 12 4 7 State: 5 {1 2 4 6 9} 10 12 5 8
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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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EOF
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cat >expected <<EOF
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@ -307,6 +319,89 @@ State: 8
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State: 9 {1}
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[0] 9
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--END--
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HOA: v1
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States: 15
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Start: 13
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AP: 2 "p1" "p0"
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Acceptance: 2 Inf(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 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 0
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State: 1 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 0
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State: 2 {0}
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[!0&!1] 10
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[0&!1] 11
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[!0&1] 2
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[0&1] 9
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State: 3 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 3
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State: 4 {0}
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 4
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[0&1] 7
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State: 5 {0}
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[!0&!1] 10
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[0&!1] 12
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[!0&1] 5
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[0&1] 8
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State: 6 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 4
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[0&1] 6
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State: 7 {0}
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 4
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[0&1] 7
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State: 8
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 8
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[0&1] 8
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[!0&1] 14
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[0&1] 14
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State: 9
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 3
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State: 10 {0}
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[!0&!1] 10
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[0&!1] 12
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[!0&1] 5
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[0&1] 8
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State: 11 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 8
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[0&1] 6
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State: 12
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 8
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[0&1] 8
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State: 13
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[!0&!1] 10
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[0&!1] 11
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[!0&1] 2
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[0&1] 3
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State: 14 {1}
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[!0&1] 14
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[0&1] 14
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--END--
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EOF
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cat >expected-tgba <<EOF
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@ -460,6 +555,90 @@ State: 8
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State: 9 {0}
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[0] 9
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--END--
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HOA: v1
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States: 15
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Start: 13
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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
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--BODY--
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State: 0 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 0
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State: 1 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 0
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State: 2 {0}
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[!0&!1] 10
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[0&!1] 11
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[!0&1] 2
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[0&1] 9
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State: 3 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 3
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State: 4 {0}
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 4
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[0&1] 7
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State: 5 {0}
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[!0&!1] 10
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[0&!1] 12
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[!0&1] 5
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[0&1] 8
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State: 6 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 4
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[0&1] 6
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State: 7 {0}
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 4
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[0&1] 7
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State: 8
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 8
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[0&1] 8
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[!0&1] 14
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[0&1] 14
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State: 9
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 1
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[0&1] 3
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State: 10 {0}
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[!0&!1] 10
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[0&!1] 12
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[!0&1] 5
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[0&1] 8
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State: 11 {0}
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[!0&!1] 12
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[0&!1] 11
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[!0&1] 8
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[0&1] 6
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State: 12
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[!0&!1] 12
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[0&!1] 12
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[!0&1] 8
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[0&1] 8
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State: 13
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[!0&!1] 10
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[0&!1] 11
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[!0&1] 2
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[0&1] 3
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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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EOF
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run 0 $autfilt -H --remove-fin test1 > output
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@ -244,6 +244,12 @@ namespace spot
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return res;
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}
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// Return the lowest acceptance mark
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mark_t lowest() const
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{
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return id & -id;
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}
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// Remove n bits that where set
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mark_t& remove_some(unsigned n)
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{
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@ -22,6 +22,7 @@
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#include <iostream>
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#include "cleanacc.hh"
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#include "totgba.hh"
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#include "mask.hh"
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//#define TRACE
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#ifdef TRACE
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@ -34,6 +35,98 @@ namespace spot
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{
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namespace
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{
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// Check whether the SCC composed of all states STATES, and
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// visiting all acceptance marks in SETS contains non-accepting
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// cycles.
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//
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// A cycle is accepting (in a Rabin automaton) if there exists an
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// acceptance pair (Fᵢ, Iᵢ) such that some states from Iᵢ are
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// visited while no states from Fᵢ are visited.
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//
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// Consequently, a cycle is non-accepting if for all acceptance
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// pairs (Fᵢ, Iᵢ), either no states from Iᵢ are visited or some
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// states from Fᵢ are visited. (This corresponds to an accepting
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// cycle with Streett acceptance.)
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bool 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 sets)
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{
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// Consider the SCC as one large cycle and check its
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// intersection with all Fᵢs and Iᵢs: This is the SETS
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// variable.
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//
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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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// 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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// non-accepting. We may have a smaller cycle that is
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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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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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// converting that SCC into a TGBA and running our emptiness
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// check. This is not a really smart implementation and
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// could be improved.
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std::vector<bool> keep(aut->num_states(), false);
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for (auto s: states)
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keep[s] = true;
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auto sccaut = mask_keep_states(aut, keep, states.front());
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// Force SBA to false. It does not affect the emptiness
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// check result, however it prevent recurring into this
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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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// of its states are final). If SCCAUT is nonempty, the SCC
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// is not DBA realizable.
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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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// been seen with seeing the mathing F₁. In this SCC any state
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// in these I₁ is therefore final. Otherwise we do not know: it
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// is possible that there is a non-accepting cycle in the SCC
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// that do not visit Fᵢ.
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std::set<unsigned> unknown;
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for (auto s: states)
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{
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if (aut->state_acc_sets(s) & i)
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final[s] = true;
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else
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unknown.insert(s);
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}
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// Check whether it is possible to build non-accepting cycles
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// using only the "unknown" states.
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while (!unknown.empty())
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{
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std::vector<bool> keep(aut->num_states(), false);
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for (auto s: unknown)
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keep[s] = true;
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scc_info si(mask_keep_states(aut, keep, *unknown.begin()));
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unsigned scc_max = si.scc_count();
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for (unsigned scc = 0; scc < scc_max; ++scc)
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{
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for (auto s: si.states_of(scc))
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unknown.erase(s);
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if (si.is_trivial(scc))
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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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return false;
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}
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}
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return true;
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}
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// If the DNF is
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// Fin(1)&Inf(2)&Inf(4) | Fin(2)&Fin(3)&Inf(1) |
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// Inf(1)&Inf(3) | Inf(1)&Inf(2) | Fin(4)
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@ -118,6 +211,50 @@ namespace spot
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if (!aut->acc().uses_fin_acceptance())
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return std::const_pointer_cast<twa_graph>(aut);
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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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std::vector<bool> scc_is_ba_type(si.scc_count(), false);
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bool ba_type = false;
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std::vector<bool> ba_final_states;
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if (aut->has_state_based_acc()
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&& aut->is_deterministic()
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&& aut->acc().is_rabin() > 0)
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{
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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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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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for (unsigned scc = 0; scc < scc_max; ++scc)
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{
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if (si.is_trivial(scc))
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{
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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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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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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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trace << scc << ": " << scc_is_ba_type[scc] << " {";
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for (auto s: si.states_of(scc))
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trace << ' ' << s;
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trace << " }\n";
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}
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#endif
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}
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std::vector<acc_cond::acc_code> code;
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std::vector<acc_cond::mark_t> rem;
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std::vector<acc_cond::mark_t> keep;
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@ -257,13 +394,14 @@ namespace spot
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for (auto c: code)
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new_code.append_or(std::move(c));
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// The condition to use for SCCs that are BA-type.
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acc_cond::mark_t final_acc = allinf.lowest();
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unsigned cs = code.size();
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for (unsigned i = 0; i < cs; ++i)
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trace << i << " Rem " << rem[i] << " Code " << code[i]
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<< " Keep " << keep[i] << '\n';
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scc_info si(aut);
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unsigned nst = aut->num_states();
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auto res = make_twa_graph(aut->get_dict());
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res->copy_ap_of(aut);
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@ -281,6 +419,22 @@ namespace spot
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trace << "SCC #" << n << " uses " << m << '\n';
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// What to keep and add into the main copy
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if (scc_is_ba_type[n])
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{
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// If the SCC is BA-type, we know exactly what state need to
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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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for (auto& t: aut->out(s))
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res->new_edge(s, t.dst, t.cond, acc);
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}
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continue;
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}
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acc_cond::mark_t main_sets = 0U;
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acc_cond::mark_t main_add = 0U;
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bool intersects_fin = false;
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@ -339,9 +493,11 @@ namespace spot
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}
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}
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}
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}
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if (ba_type)
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res->prop_state_based_acc();
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res->purge_dead_states();
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trace << "before cleanup: " << res->get_acceptance() << '\n';
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cleanup_acceptance_here(res);
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