DeepAI AI Chat
Log In Sign Up

Modular Mix-and-Match Complementation of Büchi Automata (Technical Report)

01/05/2023
by   Vojtech Havlena, et al.
0

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 BA's 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(4n) 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

05/24/2022

Register Set Automata (Technical Report)

We present register set automata (RsAs), a register automaton model over...
06/04/2022

Complementing Büchi Automata with Ranker (Technical Report)

We present the tool Ranker for complementing Büchi automata (BAs). Ranke...
07/05/2020

Proving Non-Inclusion of Büchi Automata based on Monte Carlo Sampling

The search for a proof of correctness and the search for counterexamples...
10/21/2020

Harnessing LTL With Freeze Quantification

Logics and automata models for languages over infinite alphabets, such a...
10/04/2019

Succinct Determinisation of Counting Automata via Sphere Construction (Technical Report)

We propose an efficient algorithm for determinising counting automata (C...