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Automata in Infinite-state Formal Verification
Lengál, Ondřej ; Jančar, Petr (oponent) ; Veith, Helmut (oponent) ; Esparza, Javier (oponent) ; Vojnar, Tomáš (vedoucí práce)
The work presented in this thesis focuses on finite state automata over finite words and finite trees, and the use of such automata in formal verification of infinite-state systems. First, we focus on extensions of a previously introduced framework for verifi cation of heap-manipulating programs-in particular programs with complex dynamic data structures-based on tree automata. We propose several extensions to the framework, such as making it fully automated or extending it to consider ordering over data values. Further, we also propose novel decision procedures for two logics that are often used in formal verification: separation logic and weak monadic second order logic of one successor. These decision procedures are based on a translation of the problem into the domain of automata and subsequent manipulation in the target domain. Finally, we have also developed new approaches for efficient manipulation with tree automata, mainly for testing language inclusion and for handling automata with large alphabets, and implemented them in a library for general use. The developed algorithms are used as the key technology to make the above mentioned techniques feasible in practice.
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Syntaktická analýza založená na gramatických a automatových systémech
Šoustar, Jakub ; Kocman, Radim (oponent) ; Meduna, Alexandr (vedoucí práce)
Tato práce se zabývá syntaktickou analýzou s využitím systémů paralelně komunikujících zásobníkových automatů. Zejména se zaměřuje na dopady nedeterminismu v jednotlivých komponentách na celý systém. Také je představen návrh algoritmu pro převod některých paralelně komunikujících gramatických systémů na systémy paralelně komunikujících zásobníkových automatů. Získané poznatky jsou použity při návrhu a implementaci metody syntaktické analýzy.
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Simulace a protiřetězce pro efektivní práci s konečnými automaty
Holík, Lukáš ; Černá, Ivana (oponent) ; Jančar, Petr (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well established for finite word automata. We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that is very well suited for quotienting. The combination principle is relevant also for word automata. We then generalise the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree automata. Subsequently, we improve the antichain technique for both word and tree automata by combining it with the simulation-based inclusion checking techniques, significantly improving efficiency of the antichain method. We then show how the developed reduction and inclusion checking methods improve the method of abstract regular tree model checking, the method that was the original motivation for starting the work on tree automata. Both the reduction and the language inclusion methods are based on relatively simple and general principles that can be further extended for other types of automata and related formalisms. An example is our adaptation of the reduction methods for alternating Büchi automata, which results in an efficient alternating automata size reduction technique.
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Verifikace programů s ukazateli založená na detekci vzorů
Kubíček, Jan ; Erlebach, Pavel (oponent) ; Vojnar, Tomáš (vedoucí práce)
Tato práce navazuje na výsledky studií v oblasti verifikace nekonečně stavových systémů. Konkrétně se jedná o oblast abstraktního model checkingu. Seznámili jsme se s metodou založenou na abstrakci paměťové konfigurace pomocí paměťových vzorů. Tato metoda byla navržena pro verifikaci programů pracujících s dynamickými paměťovými strukturami jako například seznamy. Na dynamické paměťové struktury je nahlíženo jako na orientované grafy. Verifikace na základě paměťových vzorů abstrahuje obecně libovolné množství vytvořených uzlů do jednoho sumarizovaného uzlu. Tím se dosáhne reprezentace obecně neukončeného grafu konečným zápisem. Poté je možno efektivně provést verifikaci nad tímto abstrahovaným grafem. V naší práci se zabýváme tvorbou modelu pro nástroj implementující verifikaci na základě paměťových vzorů. Model programu je vytvořen z podmnožiny jazyka C. Hlavním přínosem práce je automatizace tvorby modelu pro verifikaci a tím dosáhnutí úplné automatizovanosti procesu verifikace. Je tak možné verifikovat programy napsané v běžném programovacím jazyce. V této práci je diskutována syntaxe vstupního jazyka i implementační detaily překladu.
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Automata in Decision Procedures and Performance Analysis
Fiedor, Tomáš ; Barnat, Jiří (oponent) ; Radu, Iosif (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis focuses on improving the state of the art of automata-based formal analysis and verification techniques for systems with an infinite state space. In the first part of the thesis, we develop two efficient decision procedures for the WS1S logic, both of them exploiting the correspondence between formulae of WS1S logic and finite automata. We start by proposing a novel antichain-based decision procedure which is, however, limited to formulae in the prenex normal form. Later, we generalize the approach to arbitrary formulae by defining the so-called language terms and constructing an on-the-fly procedure dealing with the terms using lazy techniques. In order to achieve an efficient implementation, we propose numerous optimizations (some of these optimization are not limited to our approaches only). We evaluated both our methods with other recent state-of-the art tools. The achieved results are encouraging and show we can extend the usage of WS1S to wider classes of formulae. The second part of the thesis focuses on resource bounds analysis of heap-manipulating programs. We propose a new class of shape norms based on lengths of paths between distinct points in the heap, which we derive automatically from the analysed program. For this class of norms, we introduce a calculus capable of precisely inferring changes of the analysed norms and use it to generate a corresponding integer representation of an input program followed by dedicated state-of-the art resource bounds analysis. We implemented our approach over the shape analysis based on forest-automata, implemented in the Forester tool, and using a well-established resource bounds analyser, implemented in the Loopus tool. In our experimental evaluation, we show that we indeed obtained a powerful analyser that is able to handle some showcase examples that were never analysed fully automatically before.
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Automata in Decision Procedures and Performance Analysis
Fiedor, Tomáš ; Barnat, Jiří (oponent) ; Radu, Iosif (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis focuses on improving the state of the art of automata-based formal analysis and verification techniques for systems with an infinite state space. In the first part of the thesis, we develop two efficient decision procedures for the WS1S logic, both of them exploiting the correspondence between formulae of WS1S logic and finite automata. We start by proposing a novel antichain-based decision procedure which is, however, limited to formulae in the prenex normal form. Later, we generalize the approach to arbitrary formulae by defining the so-called language terms and constructing an on-the-fly procedure dealing with the terms using lazy techniques. In order to achieve an efficient implementation, we propose numerous optimizations (some of these optimization are not limited to our approaches only). We evaluated both our methods with other recent state-of-the art tools. The achieved results are encouraging and show we can extend the usage of WS1S to wider classes of formulae. The second part of the thesis focuses on resource bounds analysis of heap-manipulating programs. We propose a new class of shape norms based on lengths of paths between distinct points in the heap, which we derive automatically from the analysed program. For this class of norms, we introduce a calculus capable of precisely inferring changes of the analysed norms and use it to generate a corresponding integer representation of an input program followed by dedicated state-of-the art resource bounds analysis. We implemented our approach over the shape analysis based on forest-automata, implemented in the Forester tool, and using a well-established resource bounds analyser, implemented in the Loopus tool. In our experimental evaluation, we show that we indeed obtained a powerful analyser that is able to handle some showcase examples that were never analysed fully automatically before.
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Automata in Infinite-state Formal Verification
Lengál, Ondřej ; Jančar, Petr (oponent) ; Veith, Helmut (oponent) ; Esparza, Javier (oponent) ; Vojnar, Tomáš (vedoucí práce)
The work presented in this thesis focuses on finite state automata over finite words and finite trees, and the use of such automata in formal verification of infinite-state systems. First, we focus on extensions of a previously introduced framework for verifi cation of heap-manipulating programs-in particular programs with complex dynamic data structures-based on tree automata. We propose several extensions to the framework, such as making it fully automated or extending it to consider ordering over data values. Further, we also propose novel decision procedures for two logics that are often used in formal verification: separation logic and weak monadic second order logic of one successor. These decision procedures are based on a translation of the problem into the domain of automata and subsequent manipulation in the target domain. Finally, we have also developed new approaches for efficient manipulation with tree automata, mainly for testing language inclusion and for handling automata with large alphabets, and implemented them in a library for general use. The developed algorithms are used as the key technology to make the above mentioned techniques feasible in practice.
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Simulace a protiřetězce pro efektivní práci s konečnými automaty
Holík, Lukáš ; Černá, Ivana (oponent) ; Jančar, Petr (oponent) ; Vojnar, Tomáš (vedoucí práce)
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two problems that are crucial for many applications of tree automata. For size reduction of tree automata, we adapt the simulation quotient technique that is well established for finite word automata. We give efficient algorithms for computing tree automata simulations and we also introduce a new type of relation that arises from a combination of tree automata downward and upward simulation and that is very well suited for quotienting. The combination principle is relevant also for word automata. We then generalise the so called antichain universality and language inclusion checking technique developed originally for finite word automata for tree automata. Subsequently, we improve the antichain technique for both word and tree automata by combining it with the simulation-based inclusion checking techniques, significantly improving efficiency of the antichain method. We then show how the developed reduction and inclusion checking methods improve the method of abstract regular tree model checking, the method that was the original motivation for starting the work on tree automata. Both the reduction and the language inclusion methods are based on relatively simple and general principles that can be further extended for other types of automata and related formalisms. An example is our adaptation of the reduction methods for alternating Büchi automata, which results in an efficient alternating automata size reduction technique.
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Verifikace programů s ukazateli založená na detekci vzorů
Kubíček, Jan ; Erlebach, Pavel (oponent) ; Vojnar, Tomáš (vedoucí práce)
Tato práce navazuje na výsledky studií v oblasti verifikace nekonečně stavových systémů. Konkrétně se jedná o oblast abstraktního model checkingu. Seznámili jsme se s metodou založenou na abstrakci paměťové konfigurace pomocí paměťových vzorů. Tato metoda byla navržena pro verifikaci programů pracujících s dynamickými paměťovými strukturami jako například seznamy. Na dynamické paměťové struktury je nahlíženo jako na orientované grafy. Verifikace na základě paměťových vzorů abstrahuje obecně libovolné množství vytvořených uzlů do jednoho sumarizovaného uzlu. Tím se dosáhne reprezentace obecně neukončeného grafu konečným zápisem. Poté je možno efektivně provést verifikaci nad tímto abstrahovaným grafem. V naší práci se zabýváme tvorbou modelu pro nástroj implementující verifikaci na základě paměťových vzorů. Model programu je vytvořen z podmnožiny jazyka C. Hlavním přínosem práce je automatizace tvorby modelu pro verifikaci a tím dosáhnutí úplné automatizovanosti procesu verifikace. Je tak možné verifikovat programy napsané v běžném programovacím jazyce. V této práci je diskutována syntaxe vstupního jazyka i implementační detaily překladu.
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Syntaktická analýza založená na gramatických a automatových systémech
Šoustar, Jakub ; Kocman, Radim (oponent) ; Meduna, Alexandr (vedoucí práce)
Tato práce se zabývá syntaktickou analýzou s využitím systémů paralelně komunikujících zásobníkových automatů. Zejména se zaměřuje na dopady nedeterminismu v jednotlivých komponentách na celý systém. Také je představen návrh algoritmu pro převod některých paralelně komunikujících gramatických systémů na systémy paralelně komunikujících zásobníkových automatů. Získané poznatky jsou použity při návrhu a implementaci metody syntaktické analýzy.
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