Simple grammar bisimilarity, with an application to session type equivalence

TL;DR

This paper introduces a polynomial-time algorithm for simple grammar bisimilarity and applies it to efficiently decide context-free session type equivalence, improving over previous double-exponential methods.

Contribution

The authors present the first polynomial-time algorithm for simple grammar bisimilarity and its application to session type equivalence, reducing complexity from double to single exponential.

Findings

Algorithm for simple grammar bisimilarity runs in polynomial time relative to grammar valuation.

Conversion from context-free session types to simple grammars is linear in size.

Deciding context-free session type equivalence is now polynomial-time.

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 double-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.