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Deciding Logic with Automata
Hečko, Michal ; Holík, Lukáš (oponent) ; Lengál, Ondřej (vedoucí práce)
The work presented in this thesis focuses on deciding quantified linear integer arithmetic using finite automata. We present a novel implementation of the classical automata-based decision procedure supporting the SMT-LIB input format. Our comprehensive presentation of the developed tool focuses on various aspects and design decisions that play a prominent role in the performance of the implementation. We identify the lack of theory-based reasoning as the primary reason for the overall poor performance of the decision procedure and give a range of cheap heuristics that significantly improve its speed. We also give a~novel top-down reformulation of the procedure that allows to perform theory-based reasoning during the construction of automata. We also compare our tool to the state-of-the-art SMT solvers, showing that our prototype implementation is comparative and even superior to the state of the art.
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An Automata-Based Decision Procedure
Hečko, Michal ; Češka, Milan (oponent) ; Lengál, Ondřej (vedoucí práce)
Presburger arithmetics (PrA) is a decidable, first-order theory of natural numbers, with applications in many areas in formal verification of software properties. SMT-solvers tools implementing various algorithmic approaches to deciding whether a formula has a solution play a crucial role in formal verification. In this work, we document building a novel automatic SMT solver for PrA based on finite automata an approach that no SMT solver currently employs. We provide an overview of challenges and their solutions arising from the complexity of such a tool, including results from the conducted experiments already showing problems in which this alternative approach outperforms the state-of-the-art solvers. We have also identified problems in which the performance of the automata-based procedure struggles, which are open research opportunities.
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An Automata-Based Decision Procedure
Hečko, Michal ; Češka, Milan (oponent) ; Lengál, Ondřej (vedoucí práce)
Presburger arithmetics (PrA) is a decidable, first-order theory of natural numbers, with applications in many areas in formal verification of software properties. SMT-solvers tools implementing various algorithmic approaches to deciding whether a formula has a solution play a crucial role in formal verification. In this work, we document building a novel automatic SMT solver for PrA based on finite automata an approach that no SMT solver currently employs. We provide an overview of challenges and their solutions arising from the complexity of such a tool, including results from the conducted experiments already showing problems in which this alternative approach outperforms the state-of-the-art solvers. We have also identified problems in which the performance of the automata-based procedure struggles, which are open research opportunities.
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