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First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems: Automation, Formalization,
Aart Middeldorp1, Alexander Lochmann1, Fabian Mitterwallner1
1Department of Computer Science, University of Innsbruck, Innsbruck, Austria.
Journal of Automated Reasoning
|April 11, 2023
Summary
The decidability of first-order theory for linear variable-separated rewrite systems is established. A new decision procedure, implemented in the FORT tool, utilizes tree automata and has been formally verified.
Area of Science:
- Computer Science
- Formal Methods
- Automata Theory
Background:
- The first-order theory of rewriting is crucial for program analysis and verification.
- Decidability of this theory for specific classes of rewrite systems is a key research challenge.
Purpose of the Study:
- To present a novel decision procedure for the first-order theory of linear variable-separated rewrite systems.
- To introduce FORT, a tool for decision and synthesis based on this procedure.
- To enhance the expressiveness and versatility of the theory and tool.
Main Methods:
- Development of a new decision procedure based on tree automata techniques.
- Formal verification of the procedure using the Isabelle theorem prover.
- Implementation of the procedure in the FORT decision and synthesis tool.
- Design of a certificate language for verifying FORT's output using FORTify.
Main Results:
- The first-order theory of rewriting is proven decidable for linear variable-separated rewrite systems.
- The FORT tool demonstrates decision and synthesis capabilities for properties within this theory.
- Extensive experiments validate the performance and applicability of the developed methods.
Conclusions:
- The presented decision procedure and FORT tool offer a robust solution for analyzing linear variable-separated rewrite systems.
- Formal verification ensures the correctness of the decision procedure.
- The certificate language and FORTify provide a mechanism for trusted verification of results.
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