spot/doc/org/autfilt.org

autfilt

• Conversion between formats
• Displaying statistics
• Filtering automata
• Simplifying automata
• Transformations
• Examples

The autfilt tool can filter, transform, and convert a stream of automata.

The tool operates a loop over 5 phases:

• input one automaton
• optionally preprocess the automaton
• optionally filter the automaton (i.e., decide whether to ignore the automaton or continue with it)
• optionally postprocess the automaton
• output the automaton

The simplest way to use the tool is simply to use it for input and output (i.e., format conversion) without any transformation and filtering.

Conversion between formats

autfilt can read automata written in the Hanoi Omega Automata Format, as Spin never claims, using LBTT's format, or using ltl2dstar's format. Automata in those formats (even a mix of those formats) can be concatenated in the same stream, autfilt will process them in batch. (The only restriction is that inside a file an automaton in LBTT's format may not follow an automaton in ltl2dstar's format.)

The output format can be controlled using the common output options (like --spin, --lbtt, --dot, --hoaf…).

cat >example.hoa <<EOF
HOA: v1
States: 1
Start: 0
AP: 1 "p0"
Acceptance: 1 Inf(0)
--BODY--
State: 0
[0] 0 {0}
[!0] 0
--END--
EOF
autfilt example.hoa --dot

digraph G {
  rankdir=LR
  I [label="", style=invis, width=0]
  I -> 0
  0 [label="0"]
  0 -> 0 [label="p0\n{0}"]
  0 -> 0 [label="!p0"]
}

The --spin options implicitly requires a degeneralization:

autfilt example.hoa --spin

never {
accept_init:
  if
  :: ((p0)) -> goto accept_init
  :: ((!(p0))) -> goto T0_S2
  fi;
T0_S2:
  if
  :: ((p0)) -> goto accept_init
  :: ((!(p0))) -> goto T0_S2
  fi;
}

autfilt example.hoa --lbtt

1 1t
0 1
0 0 -1 p0
0 -1 ! p0
-1

Displaying statistics

One special output format of autfilt is the statistic output. For instance the following command calls randaut to generate 10 random automata, and pipe the result into autfilt to display various statistics.

randaut --hoa -n 10 -A0..2 -Q10..20 -d0.05 2 |
autfilt --stats='%s states, %e edges, %a acc-sets, %c SCCs, det=%d'

16 states, 28 edges, 1 acc-sets, 1 SCCs, det=0
19 states, 37 edges, 0 acc-sets, 1 SCCs, det=0
16 states, 24 edges, 1 acc-sets, 1 SCCs, det=0
12 states, 16 edges, 0 acc-sets, 5 SCCs, det=0
12 states, 17 edges, 2 acc-sets, 3 SCCs, det=0
15 states, 21 edges, 2 acc-sets, 5 SCCs, det=0
10 states, 12 edges, 0 acc-sets, 4 SCCs, det=1
10 states, 14 edges, 1 acc-sets, 1 SCCs, det=0
19 states, 27 edges, 1 acc-sets, 1 SCCs, det=0
11 states, 12 edges, 1 acc-sets, 9 SCCs, det=1

The following % sequences are available:

  %%                         a single %
  %A, %a                     number of acceptance pairs or sets
  %C, %c                     number of SCCs
  %d                         1 if the output is deterministic, 0 otherwise
  %E, %e                     number of edges
  %F                         name of the input file
  %n                         number of nondeterministic states in output
  %p                         1 if the output is complete, 0 otherwise
  %r                         conversion time (including post-processings, but
                             not parsing) in seconds
  %S, %s                     number of states
  %T, %t                     number of transitions

When a letter is available both as uppercase and lowercase, the uppercase version refer to the input automaton, while the lowercase refer to the output automaton. Of course this distinction makes sense only if autfilt was instructed to perform an operation on the input automaton.

Filtering automata

autfilt supports multiple ways to filter automata based on different characteristics of the automaton.

      --acc-sets=RANGE       keep automata whose number of acceptance sets are
                             in RANGE
      --are-isomorphic=FILENAME   keep automata that are isomorphic to the
                             automaton in FILENAME
      --edges=RANGE          keep automata whose number of edges are in RANGE
      --intersect=FILENAME   keep automata whose languages have an non-empty
                             intersection with the automaton from FILENAME
      --is-complete          keep complete automata
      --is-deterministic     keep deterministic automata
      --is-empty             keep automata with an empty language
      --states=RANGE         keep automata whose number of states are in RANGE
  -u, --unique               do not output the same automaton twice (same in
                             the sense that they are isomorphic)
  -v, --invert-match         select non-matching automata

For instance --states=2..5 --acc-sets=3 will keep only automata that use 3 acceptance sets, and that have between 2 and 5 states.

Except for --unique, all these filters can be inverted. Using --states=2..5 --acc-sets=3 -v will drop all automata that use 3 acceptance sets and that have between 2 and 5 states, and keep the others.

Simplifying automata

The standard set of automata simplification routines (these are often referred to as the "post-processing" routines, because these are the procedures performed by ltl2tgba after translating a formula into a TGBA) are available through the following options.

This set of options controls the desired type of output automaton:

  -B, --ba                   Büchi Automaton
      --generic              Any acceptance is allowed (default)
  -M, --monitor              Monitor (accepts all finite prefixes of the given
                             property)
      --tgba                 Transition-based Generalized Büchi Automaton

These options specifies desired properties:

  -a, --any                  no preference, do not bother making it small or
                             deterministic (default)
  -C, --complete             output a complete automaton (combine with other
                             intents)
  -D, --deterministic        prefer deterministic automata
      --small                prefer small automata
  -S, --state-based-acceptance, --sbacc
                             define the acceptance using states

Finally, the following switches control the amount of effort applied to reach the desired properties:

      --high                 all available optimizations (slow)
      --low                  minimal optimizations (fast, default)
      --medium               moderate optimizations

By default, --any --low is used, which cause all simplifications to be skipped. If you want to reduce the size of the automaton, try --small --high and if you want to try to make it deterministic (their is to guaranty of result, this is only a preference), try --deterministic --high.

Transformations

The following transformations are available:

      --cleanup-acceptance   remove unused acceptance sets from the automaton
      --cnf-acceptance       put the acceptance condition in Conjunctive Normal
                             Form
      --complement-acceptance   complement the acceptance condition (without
                             touching the automaton)
      --destut               allow less stuttering
      --dnf-acceptance       put the acceptance condition in Disjunctive Normal
                             Form
      --exclusive-ap=AP,AP,...   if any of those APs occur in the automaton,
                             restrict all edges to ensure two of them may not
                             be true at the same time.  Use this option
                             multiple times to declare independent groups of
                             exclusive propositions.
      --instut[=1|2]         allow more stuttering (two possible algorithms)
      --keep-states=NUM[,NUM...]   only keep specified states.  The first state
                             will be the new initial state.  Implies
                             --remove-unreachable-states.
      --mask-acc=NUM[,NUM...]   remove all transitions in specified acceptance
                             sets
      --merge-transitions    merge transitions with same destination and
                             acceptance
      --product=FILENAME     build the product with the automaton in FILENAME
      --randomize[=s|t]      randomize states and transitions (specify 's' or
                             't' to randomize only states or transitions)
      --remove-ap=AP[=0|=1][,AP...]
                             remove atomic propositions either by existential
                             quantification, or by assigning them 0 or 1
      --remove-dead-states   remove states that are unreachable, or that cannot
                             belong to an infinite path
      --remove-fin           rewrite the automaton without using Fin acceptance

      --remove-unreachable-states
                             remove states that are unreachable from the
                             initial state
      --separate-sets        if both Inf(x) and Fin(x) appear in the acceptance
                             condition, replace Fin(x) by a new Fin(y) and
                             adjust the automaton
      --simplify-exclusive-ap   if --exclusive-ap is used, assume those AP
                             groups are actually exclusive in the system to
                             simplify the expression of transition labels
                             (implies --merge-transitions)
      --strip-acceptance     remove the acceptance condition and all acceptance
                             sets

Examples

Here is an automaton with transition-based acceptance:

cat >aut-ex1.hoa<<EOF
HOA: v1
States: 3
Start: 0
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 4 Inf(0)&Fin(1)&Fin(3) | Inf(2)&Inf(3) | Inf(1)
--BODY--
State: 0 {3}
[t] 0
[0] 1 {1}
[!0] 2 {0}
State: 1 {3}
[1] 0
[0&1] 1 {0}
[!0&1] 2 {2}
State: 2
[!1] 0
[0&!1] 1 {0}
[!0&!1] 2 {0}
--END--
EOF

(Note: the '.' argument passed to --dot below hides default options discussed on another page, while the 'a' causes the acceptance condition to be displayed.)

autfilt aut-ex1.hoa --dot=.a

Using -S will "push" the acceptance membership of the transitions to the states:

autfilt -S aut-ex1.hoa --dot=.a

Using --cnf-acceptance simply rewrites the acceptance condition in Conjunctive Normal Form:

autfilt --cnf-acceptance aut-ex1.hoa --dot=.a

Using --remove-fin transforms the automaton to remove all traces of Fin-acceptance: this usually requires adding non-deterministic jumps to altered copies of strongly-connected components.

autfilt --remove-fin aut-ex1.hoa --dot=.a

Use --mask-acc=NUM to remove some acceptances sets and all transitions they contain. The acceptance condition will be updated to reflect the fact that these sets can never be visited.

autfilt --mask-acc=1,2 aut-ex1.hoa --dot=.a

Atomic propositions can be removed from an automaton in three ways:

• use --remove-ap=a to remove a by existential quantification, i.e., both a and its negation will be replaced by true. This does not remove any transition.
• use --remove-ap=a=0 to keep only transitions compatible with !a (i.e, transitions requiring a will be removed).
• use --remove-ap=a=1 to keep only transitions compatible with a (i.e, transitions requiring !a will be removed).

Here are the results of these three options on our example:

autfilt --remove-ap=a aut-ex1.hoa --dot=.a

autfilt --remove-ap=a=0 aut-ex1.hoa --dot=.a

autfilt --remove-ap=a=1 aut-ex1.hoa --dot=.a