Reasoning about Regular Properties: A Comparative Study

Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string constraint solving. The new algorithms demonstrated a significant potential, but they have never been systematically compared, neither among each other nor with the state-of-the art implementations of existing (non)deterministic automata-based methods. In this paper, we provide the first such comparison as well as an overview of the existing algorithms and their implementations. We collect a diverse benchmark mostly originating in or related to practical problems from string constraint solving, analysing LTL properties, and regular model checking, and evaluate collected implementations on it. The results reveal the best tools and hint on what the best algorithms and implementation techniques are. Roughly, although some advanced algorithms are fast, such as antichain algorithms and reductions to IC3/PDR, they are not as overwhelmingly dominant as sometimes presented and there is no clear winner. The simplest NFA-based technology may be actually the best choice, depending on the problem source and implementation style. Our findings should be highly relevant for development of these techniques as well as for related fields such as string constraint solving

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.

Probabilistic Bisimulation for Parameterized Systems (Technical Report)

Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot of work on verifying probabilistic bisimulation for finite systems. This is however not the case for parameterized systems, where the problem is in general undecidable. In this paper we provide a generic framework for reasoning about probabilistic bisimulation for parameterized systems. Our approach is in the spirit of software verification, wherein we encode proof rules for probabilistic bisimulation and use a decidable first-order theory to specify systems and candidate bisimulation relations, which can then be checked automatically against the proof rules. As a case study, we show that our framework is sufficiently expressive for proving the anonymity property of the parameterized dining cryptographers protocol and the parameterized grades protocol, when supplied with a candidate regular bisimulation relation. Both of these protocols hitherto could not be verified by existing automatic methods. Moreover, with the help of standard automata learning algorithms, we show that the candidate relations can be synthesized fully automatically, making the verification fully automated

Algorithmic Verification of Component-based Systems

This dissertation discusses algorithmic verification techniques for concurrent component-based systems modeled in the Behavior-Interaction-Priority (BIP) framework with both bounded and unbounded concurrency. BIP is a component framework for mixed software/hardware system design in a rigorous and correct-by-construction manner. System design is defined as a formal, accountable and coherent process for deriving trustworthy and optimised implementations from high-level system models and the corresponding execution platform descriptions. The essential properties of a system model are guaranteed at the earliest possible design phase, and a correct implementation is then automatically generated from the validated high-level system model through a sequence of property preserving model transformations, which progressively refines the model with details specific to the target execution platform. The first major contribution of this dissertation is an efficient safety verification technique for BIP system models, where the number of participating components is fixed and the data variables can have infinite domains, but their manipulation is limited to linear arithmetic. The key insight of our technique is to take advantage of the structure features of the BIP system and handle the computation in the components and coordination between the components in the verification separately. On the computation level, we apply the state-of-the-art counterexample abstraction techniques to reason about the behavior of components and explore all the possible reachable states ; while on the coordination level, we exploit both partial order techniques and symmetry reduction techniques to handle the state space explosion problem due to concurrency, and reduce the redundant interleavings of concurrent interactions. We have implemented the proposed techniques in a prototype tool and carried out a comprehensive performance evaluation on a set of BIP system models. The second major contribution of this dissertation is a uniform design and verification framework for parameterized systems based on BIP. Parameterized systems are systems consisting of homogeneous processes, and the parameter indicates the number of such processes in the system. A parameterized system, therefore, describes an infinite family of systems, where instances of the family can be obtained by fixing the value of the parameter. Verification of correctness of such systems amounts to verifying the correctness of every member of the infinite family described by the system. First of all, we propose the first order interaction logic (FOIL) as a formal language for parameterized system architectures and communication primitives. This logic is powerful enough to express architectures found in distributed systems, including the classical architectures : token-passing rings, rendezvous cliques, broadcast cliques, rendezvous stars. We also identify a fragment of FOIL that is well-suited for the specification of parameterized BIP systems and prove its decidability. Second, we provide a framework for the integration of mathematical models from the parameterized model checking literature in an automated way. With our new framework, we close the gap between the mathematical formalisms and algorithms from the parameterized verification research and the practice of parameterized verification, which is usually done by engineers who are not familiar with the details of the literature

On the Use of Quasiorders in Formal Language Theory

In this thesis we use quasiorders on words to offer a new perspective on two well-studied problems from Formal Language Theory: deciding language inclusion and manipulating the finite automata representations of regular languages. First, we present a generic quasiorder-based framework that, when instantiated with different quasiorders, yields different algorithms (some of them new) for deciding language inclusion. We then instantiate this framework to devise an efficient algorithm for searching with regular expressions on grammar-compressed text. Finally, we define a framework of quasiorder-based automata constructions to offer a new perspective on residual automata.Comment: PhD thesi