Simple grammar bisimilarity, with an application to session type equivalence

2024-07-04

arXiv.org

AI Summary

This paper addresses the bisimilarity problem for simple grammars and the equivalence checking problem for context-free session types. We present the first single-exponential-time algorithm for simple grammar bisimilarity and, via a novel linear, semantics-preserving translation from context-free session types to simple grammars, reduce the previously double-exponential bisimilarity problem to single-exponential time. Combining this translation with our algorithm yields the first polynomial-time decision procedure for context-free session type equivalence. Our main contributions are: (1) the first single-exponential-time algorithm for simple grammar bisimilarity; (2) the first linear, semantics-preserving encoding of context-free session types into simple grammars; and (3) the first polynomial-time equivalence checker for context-free session types. By integrating formal language theory, session type systems, and formal verification techniques, our approach significantly improves the scalability of type equivalence verification.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Large-scale security measurements

Abstract

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a single-exponential running time. Previously only a doubly-exponential algorithm was known. As an application, we provide a conversion from context-free session types to simple grammars whose valuation is linear in the size of the type. In this way, we provide the first polynomial-time algorithm for deciding context-free session type equivalence.

Problem

• Develops polynomial algorithm for simple grammar bisimilarity decision
• Converts context-free session types to simple grammars efficiently
• Provides first polynomial-time method for session type equivalence

Innovation

• Algorithm for simple grammar bisimilarity with polynomial complexity
• Conversion from context-free session types to simple grammars
• First polynomial-time algorithm for session type equivalence