Symbolic Automatic Relations and Their Applications to SMT and CHC Solving

Shimoda, Takumi; Kobayashi, Naoki; Sakayori, Ken; Satô, Ryôsuke

doi:10.1007/978-3-030-88806-0_20

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…Recently, Shimoda et al [38] introduced symbolic automatic relations (SARs) as a formalism to verify properties of recursive data structures. While both Mso-D and SARs rely on CHCs as a backend, they differ in motivation and purpose.…”

Section: Related Workmentioning

confidence: 99%

Reasoning About Data Trees Using CHCs

Faella

Parlato

2022

Computer Aided Verification

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Reasoning about data structures requires powerful logics supporting the combination of structural and data properties. We define a new logic called Mso-D(Monadic Second-Order logic with Data) as an extension of standard Mso on trees with predicates of the desired data logic. We also define a new class of symbolic data tree automata (Sdtas) to deal with data trees using a simple machine. Mso-D and Sdtas are both Turing-powerful, and their high expressiveness is necessary to deal with interesting data structures. We cope with undecidability by encoding Sdta executions as a system of CHCs (Constrained Horn Clauses), and solving the resulting system using off-the-shelf solvers. We also identify a fragment of Mso-D whose satisfiability can be effectively reduced to the emptiness problem for Sdtas. This fragment is very expressive since it allows us to characterize a variety of data trees from the literature, solving certain infinite-state games, etc. We implement this reduction in a prototype tool that combines an Mso decision procedure over trees (Mona) with a CHC engine (Z3), and use this tool to conduct several experiments, demonstrating the effectiveness of our approach across different problem domains.

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Section: Related Workmentioning

confidence: 99%

Reasoning About Data Trees Using CHCs

Faella

Parlato

2022

Computer Aided Verification

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Neural Network-Guided Synthesis of Recursive List Functions

Kobayashi

2023

Lecture Notes in Computer Science

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Kobayashi et al. have recently proposed NeuGuS, a framework of neural-network-guided synthesis of logical formulas or simple program fragments, where a neural network is first trained based on data, and then a logical formula over integers is constructed by using the weights and biases of the trained network as hints. The previous method was, however, restricted the class of formulas of quantifier-free linear integer arithmetic. In this paper, we propose a NeuGuS method for the synthesis of recursive predicates over lists definable by using the left fold function. To this end, we design and train a special-purpose recurrent neural network (RNN), and use the weights of the trained RNN to synthesize a recursive predicate. We have implemented the proposed method and conducted preliminary experiments to confirm the effectiveness of the method.

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Symbolic Automatic Relations and Their Applications to SMT and CHC Solving

Cited by 2 publications

References 28 publications

Reasoning About Data Trees Using CHCs

Reasoning About Data Trees Using CHCs

Neural Network-Guided Synthesis of Recursive List Functions

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