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.

Parity and generalised Büchi automata - determinisation and complementation

In this thesis, we study the problems of determinisation and complementation of finite automata on infinite words. We focus on two classes of automata that occur naturally: generalised Büchi automata and nondeterministic parity automata. Generalised Büchi and parity automata occur naturally in model-checking, realisability checking and synthesis procedures. We first review a tight determinisation procedure for Büchi automata, which uses a simplification of Safra trees called history trees. As Büchi automata are special types of both generalised Büchi and parity automata, we adjust the data structure to arrive at suitably tight determinisation constructions for both generalised Büchi and parity automata. As the parity condition describes combinations of Büchi and CoBüchi conditions, instead of immediately modifying the data structure to handle parity automata, we arrive at a suitable data structure by first looking at a special case, Rabin automata with one accepting pair. One pair Rabin automata correspond to parity automata with three priorities and serve as a starting point to modify the structures that result from Büchi determinisation: we then nest these structures to reflect the standard parity condition and describe a direct determinisation construction. The generalised Büchi condition is characterised by an accepting family with 'k' accepting sets. It is easy to extend classic determinisation constructions to handle generalised Büchi automata by incorporating the degeneralization algorithm in the determinisation construction. We extend the tight Büchi construction to do exactly this. Our determinisation constructions go to deterministic Rabin automata. It is known that one can determinise to the more convenient parity condition by incorporating the standard Latest Appearance Record construction in the determinisation procedure. We determinise to parity automata using this technique. We prove lower bounds on these constructions. In the case of determinisation to Rabin automata, our constructions are tight to the state. In the case of determinisation to parity, there is a constant factor ≤ 1.5 between upper and lower bounds reducing to optimal(to the state) in the case of Büchi and 1-pair Rabin. We also reconnect tight determinisation and complementation and provide constructions for complementing generalised Büchi and parity automata by starting withour data structure for determinisation. We introduce suitable data structures for the complementation procedures based on the data structure used for determinisation. We prove lower bounds for both constructions that are tight upto an O(n) factor where 'n' is the number of states of the nondeterministic automaton that is complemented

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tool for Büchi Automata

Tato práce zpracovává problematiku Büchiho automatů a představuje knihovnu, umožňující provádět základní operace nad těmito automaty. V práci jsou uvedeny základy teorie automatů. Ty jsou použity při popisu konečných automatů, mezi které patří Büchiho automaty, jejichž popis tvoří hlavní část zde uvedené teorie. Znalost jejich vlastností je důležitá pro pochopení algoritmů, které s nimi pracují. Dále jsou tyto algoritmy představeny i s detailním vysvětlením. Následuje návrh datových struktur formátu, v jakém jsou automaty ukládány na disk. Stěžejní část práce se věnuje implementaci knihovny a pomocných skriptů. Detailně jsou zde popsány důležité nebo zajímavé části implementace jednotlivých metod. Závěr práce je věnován testování funkčnosti knihovny.This thesis elaborates the Büchi automata theory and introduces a library that enables working with them. Basics of the automata theory is explained. The main part of this work is focused on Büchi automata, which belong to finite automata. The main properties of Büchi automata are explained and proved. The knowledge of those properties is important for understanding the algorithms mentioned in this work. The next part describes those algorithms and explains their principles in details. The design of library is described in the next part of this work. Main part is aimed at the implementation of the library and auxiliary scripts. The most interesting and important parts of methods are described in detail. Closing part describes testing of library functionality.

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book