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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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Harnessing Forest Automata for Verification of Heap Manipulating Programs
Šimáček, Jiří ; Abdulla, Parosh (oponent) ; Křetínský, Mojmír (oponent) ; Vojnar, Tomáš (vedoucí práce)
This work addresses verification of infinite-state systems, more specifically, verification of programs manipulating complex dynamic linked data structures. Many different approaches emerged to date, but none of them provides a~sufficiently robust solution which would succeed in all possible scenarios appearing in practice. Therefore, in this work, we propose a new approach which aims at improving the current state of the art in several dimensions. Our approach is based on using tree automata, but it is also partially inspired by some ideas taken from the methods based on separation logic. Apart from that, we also present multiple advancements within the implementation of various tree automata operations, crucial for our verification method to succeed in practice. Namely, we provide an optimised algorithm for computing simulations over labelled transition systems which then translates into more efficient computation of simulations over tree automata. We also give a new algorithm for checking inclusion over tree automata, and we provide experimental evaluation demonstrating
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Harnessing Forest Automata for Verification of Heap Manipulating Programs
Šimáček, Jiří ; Abdulla, Parosh (oponent) ; Křetínský, Mojmír (oponent) ; Vojnar, Tomáš (vedoucí práce)
This work addresses verification of infinite-state systems, more specifically, verification of programs manipulating complex dynamic linked data structures. Many different approaches emerged to date, but none of them provides a~sufficiently robust solution which would succeed in all possible scenarios appearing in practice. Therefore, in this work, we propose a new approach which aims at improving the current state of the art in several dimensions. Our approach is based on using tree automata, but it is also partially inspired by some ideas taken from the methods based on separation logic. Apart from that, we also present multiple advancements within the implementation of various tree automata operations, crucial for our verification method to succeed in practice. Namely, we provide an optimised algorithm for computing simulations over labelled transition systems which then translates into more efficient computation of simulations over tree automata. We also give a new algorithm for checking inclusion over tree automata, and we provide experimental evaluation demonstrating
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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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