Safety and Liveness of Quantitative Automata

The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications

Safety and Liveness of Quantitative Automata

The safety-liveness dichotomy is a fundamental concept in formal languages which plays a key role in verification. Recently, this dichotomy has been lifted to quantitative properties, which are arbitrary functions from infinite words to partially-ordered domains. We look into harnessing the dichotomy for the specific classes of quantitative properties expressed by quantitative automata. These automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. In this automata-theoretic setting, we establish a connection between quantitative safety and topological continuity and provide an alternative characterization of quantitative safety and liveness in terms of their boolean counterparts. For all common value functions, we show how the safety closure of a quantitative automaton can be constructed in PTime, and we provide PSpace-complete checks of whether a given quantitative automaton is safe or live, with the exception of LimInfAvg and LimSupAvg automata, for which the safety check is in ExpSpace. Moreover, for deterministic Sup, LimInf, and LimSup automata, we give PTime decompositions into safe and live automata. These decompositions enable the separation of techniques for safety and liveness verification for quantitative specifications.Comment: Full version of the paper to appear in CONCUR 202

Playing with Trees and Logic

This document proposes an overview of my research sinc

Efficient Automata Techniques and Their Applications

Tato práce se zabývá vývojem efektivních technik pro konečné automaty a jejich aplikace. Zejména se věnujeme konečným automatům použitých pří detekci útoků v síťovém provozu a automatům v rozhodovacích procedurách a verifikaci. V první části práce navrhujeme techniky přibližné redukce nedeterministických automatů, které snižují spotřebu zdrojů v hardwarově akcelerovaném zkoumání obsahu paketů. Druhá část práce je je věnována automatům v rozhodovacích procedurách, zejména slabé monadické logice druhého řádů k následníků (WSkS) a teorie nad řetězci. Navrhujeme novou rozhodovací proceduru pro WS2S založenou na automatových termech, umožňující efektivně prořezávat stavový prostor. Dále studujeme techniky předzpracování WSkS formulí za účelem snížení velikosti konstruovaných automatů. Automaty jsme také aplikovali v rozhodovací proceduře teorie nad řetězci pro efektivní reprezentaci důkazového stromu. V poslední části práce potom navrhujeme optimalizace rank-based komplementace Buchiho automatů, které snižuje počet generovaných stavů během konstrukce komplementu.This thesis develops efficient techniques for finite automata and their applications. In particular, we focus on finite automata in network intrusion detection and automata in decision procedures and verification. In the first part of the thesis, we propose techniques of approximate reduction of nondeterministic automata decreasing consumption of resources of hardware-accelerated deep packet inspection. The second part is devoted to automata in decision procedures, in particular, to weak monadic second-order logic of k successors (WSkS) and the theory of strings. We propose a novel decision procedure for WS2S based on automata terms allowing one to effectively prune the state space. Further, we study techniques of WSkS formulae preprocessing intended to reduce the sizes of constructed intermediate automata. Moreover, we employ automata in a decision procedure of the theory of strings for efficient handling of the proof graph. The last part of the thesis then proposes optimizations in rank-based Buchi automata complementation reducing the number of generated states during the construction.