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Automata in Verification
Šmahlíková, Barbora ; Holík, Lukáš (oponent) ; Lengál, Ondřej (vedoucí práce)
Regular model checking is an automata-based technique used for verification of infinite-state systems. The configurations of a system are encoded as a finite automaton and transitions between these configurations as a finite transducer. A technique for verifying arbitrary properties of parameterized systems specified in a temporal logic LTL(MSO) has already been introduced. We present an extension of this algorithm allowing verification of hyperproperties of parameterized systems where an explicit quantification over multiple execution traces is allowed. We specify conditions that need to hold for a pair of advice bits (a finite automaton and a finite transducer) that serves as a witness of the fact that the property holds in the system. The technique presented in this work is implemented in our tool ParaHyper - the only existing tool for the verification of hyperproperties of parameterized systems. The tool uses a SAT solver to generate automata and transducers. If a pair satisfying the conditions for advice bits is found, the property holds in the system. We performed an experimental evaluation of our approach and found that ParaHyper is able to generate advice bits for formulae with an alphabet up to 4 symbols if both the automaton and the transducer have at most 2 states. When a candidate pair is given by the user, ParaHyper can, however, efficiently check if it satisfies the conditions for advice bits even for larger alphabets and greater number of states.
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Next Generation of Rank-Based Algorithms for Omega Automata
Šmahlíková, Barbora ; Holík, Lukáš (oponent) ; Lengál, Ondřej (vedoucí práce)
Büchi automata (BA) complementation is a crucial operation for termination analysis of programs, model checking, or decision procedures for various logics. Despite its prominence, practically efficient algorithms for BA complementation are still missing. This thesis deals with optimizations of Büchi automata complementation, focusing mainly on rank-based techniques. The original rank-based algorithm is asymptotically optimal, but it can still generate unnecessarily large state space. For a practical usage, it is therefore desirable to reduce the number of generated states in the complement as much as possible. We propose several techniques that can efficiently complement some special types of Büchi automata, occuring often in practice, based on their structure. Some of these techniques can also, to a certain degree, be extended to general Büchi automata. The developed techniques were implemented as an extension of the tool Ranker for Büchi automata complementation and evaluated on thousands of hard automata. Our optimizations significantly reduce the generated state space and Ranker produces in the majority of cases a~smaller complement than other state-of-the-art tools.
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Next Generation of Rank-Based Algorithms for Omega Automata
Šmahlíková, Barbora ; Holík, Lukáš (oponent) ; Lengál, Ondřej (vedoucí práce)
Büchi automata (BA) complementation is a crucial operation for termination analysis of programs, model checking, or decision procedures for various logics. Despite its prominence, practically efficient algorithms for BA complementation are still missing. This thesis deals with optimizations of Büchi automata complementation, focusing mainly on rank-based techniques. The original rank-based algorithm is asymptotically optimal, but it can still generate unnecessarily large state space. For a practical usage, it is therefore desirable to reduce the number of generated states in the complement as much as possible. We propose several techniques that can efficiently complement some special types of Büchi automata, occuring often in practice, based on their structure. Some of these techniques can also, to a certain degree, be extended to general Büchi automata. The developed techniques were implemented as an extension of the tool Ranker for Büchi automata complementation and evaluated on thousands of hard automata. Our optimizations significantly reduce the generated state space and Ranker produces in the majority of cases a~smaller complement than other state-of-the-art tools.
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