autfilt
Table of Contents
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 node [shape="circle"] 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_S1 fi; T0_S1: if :: (p0) -> goto accept_init :: (!(p0)) -> goto T0_S1 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, 30 edges, 1 acc-sets, 3 SCCs, det=0 20 states, 42 edges, 2 acc-sets, 1 SCCs, det=0 15 states, 27 edges, 2 acc-sets, 1 SCCs, det=0 10 states, 17 edges, 1 acc-sets, 1 SCCs, det=1 13 states, 25 edges, 1 acc-sets, 1 SCCs, det=0 11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0 19 states, 41 edges, 2 acc-sets, 1 SCCs, det=0 11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0 12 states, 21 edges, 1 acc-sets, 5 SCCs, det=0 18 states, 37 edges, 1 acc-sets, 5 SCCs, det=0
The following %
sequences are available:
%% a single % %A, %a number of acceptance 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 %G, %g acceptance condition (in HOA syntax) %L location in the input file %M, %m name of the automaton %n number of nondeterministic states in output %p 1 if the output is complete, 0 otherwise %r processing time (excluding parsing) in seconds %S, %s number of states %T, %t number of transitions %w one word accepted by the output automaton
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 --is-unambiguous keep only unambiguous automata --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 (with state-based acceptance) --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, --product-and=FILENAME build the product with the automaton in FILENAME to intersect languages --product-or=FILENAME build the product with the automaton in FILENAME to sum languages --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 --sat-minimize[=options] minimize the automaton using a SAT solver (only work for deterministic automata) --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 removea
by existential quantification, i.e., botha
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 requiringa
will be removed). - use
--remove-ap=a=1
to keep only transitions compatible witha
(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