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HAVLENA, V. ŠMAHLÍKOVÁ, B. LENGÁL, O. LI, Y. TURRINI, A.
Original Title
Modular Mix-and-Match Complementation of Büchi Automata
Type
conference paper
Language
English
Original Abstract
Complementation of nondeterministic Büchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of some logics. We build on ideas from a recent work on BA determinization by Li et al. and propose a new modular algorithm for BA complementation. Our algorithm allows to combine several BA complementation procedures together, with one procedure for a subset of the BAs strongly connected components (SCCs). In this way, one can exploit the structure of particular SCCs (such as when they are inherently weak or deterministic) and use more efficient specialized algorithms, regardless of the structure of the whole BA. We give a general framework into which partial complementation procedures can be plugged in, and its instantiation with several algorithms. The framework can, in general, produce a complement with an Emerson-Lei acceptance condition, which can often be more compact. Using the algorithm, we were able to establish an exponentially better new upper bound of O(4^n) for complementation of the recently introduced class of elevator automata. We implemented the algorithm in a prototype and performed a comprehensive set of experiments on a large set of benchmarks, showing that our framework complements well the state of the art and that it can serve as a basis for future efficient BA complementation and inclusion checking algorithms.
Keywords
Büchi automata, omega regular languages, complementation
Authors
HAVLENA, V.; ŠMAHLÍKOVÁ, B.; LENGÁL, O.; LI, Y.; TURRINI, A.
Released
22. 4. 2023
Publisher
Springer Verlag
Location
Paris
ISBN
0302-9743
Periodical
Lecture Notes in Computer Science
Number
13993
State
Federal Republic of Germany
Pages from
249
Pages to
270
Pages count
22
BibTex
@inproceedings{BUT182441, author="HAVLENA, V. and ŠMAHLÍKOVÁ, B. and LENGÁL, O. and LI, Y. and TURRINI, A.", title="Modular Mix-and-Match Complementation of Büchi Automata", booktitle="Proceedings of TACAS'23", year="2023", journal="Lecture Notes in Computer Science", number="13993", pages="249--270", publisher="Springer Verlag", address="Paris", issn="0302-9743" }