Table of Contents


autfilt - filter, convert, and transform omega-automata


autfilt [OPTION...] [FILENAME[/COL]...]


Convert, transform, and filter omega-automata.


-F, --file=FILENAME

process the automaton in FILENAME


If false, properties listed in HOA files are ignored, unless they can be easily verified. If true (the default) any supported property is trusted.

Output automaton type:

-b, --buchi, --Buchi

automaton with Büchi acceptance

-B, --sba, --ba

state-based Büchi Automaton (same as -S -b)

--cobuchi, --coBuchi

automaton with co-Büchi acceptance (will recognize a superset of the input language if not co-Büchi realizable)

-C, --complete

output a complete automaton

-G, --generic

any acceptance is allowed (default)

-M, --monitor

Monitor (accepts all finite prefixes of the given property)

-p, --colored-parity[=any|min|max|odd|even|min odd|min even|max odd|max


colored automaton with parity acceptance

-P, --parity[=any|min|max|odd|even|min odd|min even|max odd|max even]

automaton with parity acceptance

-S, --state-based-acceptance, --sbacc

define the acceptance using states

--tgba, --gba

automaton with Generalized Büchi acceptance

Output format:

-8, --utf8

enable UTF-8 characters in output (ignored with --lbtt or --spin)

-c, --count

print only a count of matched automata


test for the additional property PROP and output the result in the HOA format (implies -H). PROP may be some prefix of ’all’ (default), ’unambiguous’, ’stutter-invariant’, ’stutter-sensitive-example’, ’semi-determinism’, or ’strength’.

-d, --dot[=1|a|A|b|B|c|C(COLOR)|e|E|f(FONT)|h|i(ID)|k|K|n|N|o|r|R|s|t|

GraphViz’s format. Add letters for (1) force numbered states, (a) show acceptance condition (default), (A) hide acceptance condition, (b) acceptance sets as bullets, (B) bullets except for Büchi/co-Büchi automata, (c) force circular nodes, (C) color nodes with COLOR, (d) show origins when known, (e) force elliptic nodes, (E) force rEctangular nodes, (f(FONT)) use FONT, (g) hide edge labels, (h) horizontal layout, (i) or (i(GRAPHID)) add IDs, (k) use state labels when possible, (K) use transition labels (default), (n) show name, (N) hide name, (o) ordered transitions, (r) rainbow colors for acceptance sets, (R) color acceptance sets by Inf/Fin, (s) with SCCs, (t) force transition-based acceptance, (u) hide true states, (v) vertical layout, (y) split universal edges by color, (+INT) add INT to all set numbers, (<INT) display at most INT states, (#) show internal edge numbers

-H, --hoaf[=1.1|i|k|l|m|s|t|v]

Output the automaton in HOA format (default). Add letters to select (1.1) version 1.1 of the format, (i) use implicit labels for complete deterministic automata, (s) prefer state-based acceptance when possible [default], (t) force transition-based acceptance, (m) mix state and transition-based acceptance, (k) use state labels when possible, (l) single-line output, (v) verbose properties


LBTT’s format (add =t to force transition-based acceptance even on Büchi automata)

-n, --max-count=NUM

output at most NUM automata


set the name of the output automaton

-o, --output=FORMAT

send output to a file named FORMAT instead of standard output. The first automaton sent to a file truncates it unless FORMAT starts with ’>>’.

-q, --quiet

suppress all normal output

-s, --spin[=6|c]

Spin neverclaim (implies --ba). Add letters to select (6) Spin’s 6.2.4 style, (c) comments on states

--stats=FORMAT, --format=FORMAT

output statistics about the automaton

Any FORMAT string may use the following interpreted sequences (capitals for input, minuscules for output):


a single %


the part of the line before the automaton if it comes from a column extracted from a CSV file


the part of the line after the automaton if it comes from a column extracted from a CSV file

%A, %a

number of acceptance sets

%C, %c, %[LETTERS]C, %[LETTERS]c

number of SCCs; you may filter the SCCs to count using the following LETTERS, possibly concatenated: (a) accepting, (r) rejecting, (c) complete, (v) trivial, (t) terminal, (w) weak, (iw) inherently weak. Use uppercase letters to negate them.

%D, %d

1 if the automaton is deterministic, 0 otherwise

%E, %e

number of reachable edges


name of the input file

%G, %g, %[LETTERS]G, %[LETTERS]g

acceptance condition (in HOA syntax); add brackets to print an acceptance name instead and LETTERS to tweak the format: (0) no parameters, (a) accentuated, (b) abbreviated, (d) style used in dot output, (g) no generalized parameter, (l) recognize Street-like and Rabin-like, (m) no main parameter, (p) no parity parameter, (o) name unknown acceptance as ’other’, (s) shorthand for ’lo0’.

%H, %h

the automaton in HOA format on a single line (use %[opt]H or %[opt]h to specify additional options as in --hoa=opt)


location in the input file

%M, %m

name of the automaton

%N, %n

number of nondeterministic states

%P, %p

1 if the automaton is complete, 0 otherwise


wall-clock time elapsed in seconds (excluding parsing)


CPU time (excluding parsing), in seconds; Add LETTERS to restrict to(u) user time, (s) system time, (p) parent process, or (c) children processes.

%S, %s

number of reachable states

%T, %t

number of reachable transitions

%U, %u, %[LETTER]U, %[LETTER]u

1 if the automaton contains some universal

branching (or a number of [s]tates or [e]dges with

universal branching)

%W, %w

one word accepted by the automaton

%X, %x, %[LETTERS]X, %[LETTERS]x

number of atomic propositions declared in the automaton; add LETTERS to list atomic propositions with (n) no quoting, (s) occasional double-quotes with C-style escape, (d) double-quotes with C-style escape, (c) double-quotes with CSV-style escape, (p) between parentheses, any extra non-alphanumeric character will be used to separate propositions

Filtering options:

--acc-sccs=RANGE, --accepting-sccs=RANGE

keep automata whose number of non-trivial accepting SCCs is in RANGE


keep automata whose number of acceptance sets is in RANGE


keep automata that accept WORD


match automata with given acceptance condition


match automata with a number of (declared) atomic propositions in RANGE


keep automata that are isomorphic to the automaton in FILENAME


keep automata whose number of edges is in RANGE


keep automata that are equivalent (language-wise) to the automaton in FILENAME


keep automata that use existential branching (i.e., make non-deterministic choices)


keep alternating automata that use universal branching

--included-in=FILENAME keep automata whose languages are included in

of the automaton from FILENAME


keep automata whose number of accepting inherently-weak SCCs is in RANGE. An accepting SCC is inherently weak if it does not have a rejecting cycle.


keep automata whose languages have an non-empty intersection with the automaton from FILENAME


keep only automata using universal branching


keep colored automata (i.e., exactly one acceptance mark per transition or state)


keep complete automata


keep deterministic automata


keep automata with an empty language


keep only inherently weak automata


keep semi-deterministic automata

--is-stutter-invariant keep automata representing stutter-invariant



keep only terminal automata


keep only unambiguous automata


keep only very-weak automata


keep only weak automata


keep automata whose number of nondeterministic states is in RANGE

-N, --nth=RANGE

assuming input automata are numbered from 1, keep only those in RANGE

--rej-sccs=RANGE, --rejecting-sccs=RANGE

keep automata whose number of non-trivial rejecting SCCs is in RANGE


keep automata that reject WORD


keep automata whose number of SCCs is in RANGE


keep automata whose number of states is in RANGE


keep automata whose number of accepting terminal SCCs is in RANGE. Terminal SCCs are weak and complete.

--triv-sccs=RANGE, --trivial-sccs=RANGE

keep automata whose number of trivial SCCs is in RANGE


match automata with a number of declared, but unused atomic propositions in RANGE


match automata with a number of used atomic propositions 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


keep automata whose number of accepting weak SCCs is in RANGE. In a weak SCC, all transitions belong to the same acceptance sets.

RANGE may have one of the following forms: ’INT’, ’INT..INT’, ’..INT’, or ’INT..’

WORD is lasso-shaped and written as ’BF;BF;...;BF;cycle{BF;...;BF}’ where BF are arbitrary Boolean formulas. The ’cycle{...}’ part is mandatory, but the prefix can be omitted.



remove unused acceptance sets from the automaton


put the acceptance condition in Conjunctive Normal Form


complement each automaton (different strategies are used)


complement the acceptance condition (without touching the automaton)

--decompose-scc=t|w|s|N|aN, --decompose-strength=t|w|s|N|aN

extract the (t) terminal, (w) weak, or (s) strong part of an automaton or (N) the subautomaton leading to the Nth SCC, or (aN) to the Nth accepting SCC (option can be combined with commas to extract multiple parts)


allow less stuttering


put the acceptance condition in Disjunctive Normal Form


dualize each automaton


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.

--generalized-rabin[=unique-inf|share-inf], --gra[=unique-inf|

rewrite the acceptance condition as generalized Rabin; the default "unique-inf" option uses the generalized Rabin definition from the HOA format; the "share-inf" option allows clauses to share Inf sets, therefore reducing the number of sets

--generalized-streett[=unique-fin|share-fin], --gsa[=unique-fin|

rewrite the acceptance condition as generalized Streett; the "share-fin" option allows clauses to share Fin sets, therefore reducing the number of sets; the default "unique-fin" does not


allow more stuttering (two possible algorithms)


only keep specified states. The first state will be the new initial state. Implies --remove-unreachable-states.


mark the specified states as dead (no successor), and remove them. Implies --remove-dead-states.


remove all transitions in specified acceptance sets


merge transitions with same destination and acceptance


Degeneralize automata according to sets NUM1,NUM2,... If no sets are given, partial degeneralization is performed for all conjunctions of Inf and disjunctions of Fin.

--product=FILENAME, --product-and=FILENAME

build the product with the automaton in FILENAME to intersect languages


build the product with the automaton in FILENAME to sum languages


randomize states and transitions (specify ’s’ or ’t’ to randomize only states or transitions)


remove atomic propositions either by existential quantification, or by assigning them 0 or 1


remove states that are unreachable, or that cannot belong to an infinite path


rewrite the automaton without using Fin acceptance


remove states that are unreachable from the initial state


remove declared atomic propositions that are not used


minimize the automaton using a SAT solver (only works for deterministic automata). Supported options are acc=STRING, states=N, max-states=N, sat-incr=N, sat-incr-steps=N, sat-langmap, sat-naive, colored, preproc=N. Spot uses by default its PicoSAT distribution but an external SATsolver can be set thanks to the SPOT_SATSOLVER environment variable(see spot-x).


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 the acceptance condition by merging identical acceptance sets and by simplifying some terms containing complementary sets


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)


split edges into transitions labeled by conjunctions of all atomic propositions, so they can be read as letters


convert to an automaton with Streett-like acceptance. Works only with acceptance condition in DNF


remove the acceptance condition and all acceptance sets

--sum=FILENAME, --sum-or=FILENAME

build the sum with the automaton in FILENAME to sum languages


build the sum with the automaton in FILENAME to intersect languages

Decorations (for -d and -H1.1 output):


highlight one accepting run using color NUM


highlight states that recognize identical languages


highlight nondeterministic states and edges with color NUM


highlight nondeterministic edges with color NUM


highlight nondeterministic states with color NUM


highlight one run matching WORD using color NUM

Simplification goal:

-a, --any

no preference, do not bother making it small or deterministic

-D, --deterministic

prefer deterministic automata (combine with --generic to be sure to obtain a deterministic automaton)


prefer small automata

Simplification level:


all available optimizations (slow)


minimal optimizations (fast)


moderate optimizations

If any option among --small, --deterministic, or --any is given, then the simplification level defaults to --high unless specified otherwise. If any option among --low, --medium, or --high is given, then the simplification goal defaults to --small unless specified otherwise. If none of those options are specified, then autfilt acts as is --any --low were given: these actually disable the simplification routines.

Miscellaneous options:


seed for the random number generator (0)

-x, --extra-options=OPTS

fine-tuning options (see spot-x (7))


print this help


print program version

Mandatory or optional arguments to long options are also mandatory or optional for any corresponding short options.

Exit status:


if some automata were output


if no automata were output (no match)


if any error has been reported


By default, SAT-based minimization executes a binary search, checking N/2 etc. The upper bound being N (the size of the starting automaton), the lower bound is always 1 except when sat-langmap option is used.


DOUBLEQUOTEDSTRING is an acceptance formula in the HOA syntax, or a parametrized acceptance name (the different acc-name: options from HOA).


force all transitions (or all states if -S is used) to belong to exactly one acceptance condition.


M is an upper-bound on the maximum number of states of the constructed automaton.


use an incremental approach for SAT-based minimization algorithm. M can be either 1 or 2. They correspond respectively to -x sat-minimize=2 and -x sat-minimize=3 options. They restart the encoding only after (N-1)-sat-incr-steps states have been won. Each iterations of both starts by encoding the research of an N-1 automaton, N being the size of the starting automaton. 1 uses Picosat assumptions. It additionally assumes that the last sat-incr-steps states are unnecessary. On failure, it relax the assumptions to do a binary search between N-1 and (N-1)-sat-incr-steps. sat-incr-steps defaults to 6. 2, as for it, after an N-1 state automaton has been found, uses incremental solving for the next sat-incr-steps iterations by forbidding the usage of an additional state without reencoding the problem again. A full encoding occurs after sat-incr-steps iterations unless sat-incr-steps=-1 (see SPOT_XCNF environment variable described in spot-x). It defaults to 2.


set the value of sat-incr-steps to M. This is used by sat-incr option.


use the naive algorithm to find a smaller automaton. It starts from N (N being the size of the starting automaton) and then checks N-1, N-2, etc. until the last successful check.


Find the lower bound of default sat-minimize procedure (1). This relies on the fact that the size of the minimal automaton is at least equal to the total number of different languages recognized by the automaton’s states.


M is a fixed number of states to use in the result (all the states needs not be accessible in the result. Therefore, the output might be smaller nonetheless). The SAT-based procedure is just used once to synthesize one automaton, and no further minimization is attempted.


The following papers are related to some of the transformations implemented in autfilt.

Etienne Renault, Alexandre Duret-Lutz, Fabrice Kordon, and Denis Poitrenaud: Strength-based decomposition of the property Büchi automaton for faster model checking. Proceedings of TACAS’13. LNCS 7795.

The --strength-decompose option implements the definitions given in the above paper.

František Blahoudek, Alexandre Duret-Lutz, Vojtčech Rujbr, and Jan Strejček: On refinement of Büchi automata for explicit model checking. Proceedings of SPIN’15. LNCS 9232.

That paper gives the motivation for options --exclusive-ap and --simplify-exclusive-ap.

Thibaud Michaud and Alexandre Duret-Lutz: Practical stutter-invariance checks for ω-regular languages. Proceedings of SPIN’15. LNCS 9232.

Describes the algorithms used by the --destut and --instut options. These options correpond respectively to cl() and sl() in the paper.

Souheib Baarir and Alexandre Duret-Lutz: SAT-based minimization of deterministic ω-automata. Proceedings of LPAR’15 (a.k.a LPAR-20). LNCS 9450.

Describes the --sat-minimize option.


Report bugs to <spot@lrde.epita.fr>.


Copyright © 2022 Laboratoire de Recherche et Développement de l’Epita. License GPLv3+: GNU GPL version 3 or later.
This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.


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