arXiv subjects

Anton Pirogov

Publications and source records attributed to Anton Pirogov.

5 recordsLinked to original sources

arXiv2020

Ambiguity, Weakness, and Regularity in Probabilistic Büchi Automata

Probabilistic Büchi automata are a natural generalization of PFA to infinite words, but have been studied in-depth only rather recently and many interesting questions are still open. PBA are known to accept, in general, a class of languages that goes beyond the regular languages. In this work we extend the known classes of restricted PBA which are still regular, strongly relying on notions concerning ambiguity in classical omega-automata. Furthermore, we investigate the expressivity of the not yet considered but natural class of weak PBA, and we also show that the regularity problem for weak PBA is undecidable.

cs.FL↗

arXiv2019

New Optimizations and Heuristics for Determinization of Büchi Automata

In this work, we present multiple new optimizations and heuristics for the determinization of Büchi automata that exploit a number of semantic and structural properties, most of which may be applied together with any determinization procedure. We built a prototype implementation where all the presented heuristics can be freely combined and evaluated them, comparing our implementation with the state-of-the-art tool spot on multiple data sets with different characteristics. Our results show that the proposed optimizations and heuristics can in some cases significantly decrease the size of the resulting deterministic automaton.

cs.FL↗

arXiv2019

Determinization of Büchi Automata: Unifying the Approaches of Safra and Muller-Schupp

Determinization of Büchi automata is a long-known difficult problem and after the seminal result of Safra, who developed the first asymptotically optimal construction from Büchi into Rabin automata, much work went into improving, simplifying or avoiding Safra's construction. A different, less known determinization construction was derived by Muller and Schupp and appears to be unrelated to Safra's construction on the first sight. In this paper we propose a new meta-construction from nondeterministic Büchi to deterministic parity automata which strictly subsumes both the construction of Safra and the construction of Muller and Schupp. It is based on a correspondence between structures that are encoded in the macrostates of the determinization procedures - Safra trees on one hand, and levels of the split-tree, which underlies the Muller and Schupp construction, on the other. Our construction allows for combining the mentioned constructions and opens up new directions for the development of heuristics.

cs.FL↗

arXiv2019

Flat Model Checking for Counting LTL Using Quantifier-Free Presburger Arithmetic

This paper presents an approximation approach to verifying counter systems with respect to properties formulated in an expressive counting extension of linear temporal logic. It can express, e.g., that the number of acknowledgements never exceeds the number of requests to a service, by counting specific positions along a run and imposing arithmetic constraints. The addressed problem is undecidable and therefore solved on flat under-approximations of a system. This provides a flexibly adjustable trade-off between exhaustiveness and computational effort, similar to bounded model checking. Recent techniques and results for model-checking frequency properties over flat Kripke structures are lifted and employed to construct a parametrised encoding of the (approximated) problem in quantifier-free Presburger arithmetic. A prototype implementation based on the z3 SMT solver demonstrates the effectiveness of the approach based on problems from the RERS Challange.

cs.LO↗

arXiv2018

On finitely ambiguous Büchi automata

Unambiguous Büchi automata, i.e. Büchi automata allowing only one accepting run per word, are a useful restriction of Büchi automata that is well-suited for probabilistic model-checking. In this paper we propose a more permissive variant, namely finitely ambiguous Büchi automata, a generalisation where each word has at most $k$ accepting runs, for some fixed $k$. We adapt existing notions and results concerning finite and bounded ambiguity of finite automata to the setting of $ω$-languages and present a translation from arbitrary nondeterministic Büchi automata with $n$ states to finitely ambiguous automata with at most $3^n$ states and at most $n$ accepting runs per word.

cs.FL↗