Multi-Buffer Simulations for Trace Language Inclusion

TL;DR

This paper introduces multi-buffer simulation games on Büchi automata to approximate language inclusion, analyzing their decidability and complexity, and providing conditions for Duplicator's winning strategies.

Contribution

It proposes a novel multi-buffer simulation framework for Büchi automata, exploring decidability, complexity, and conditions for winning strategies, advancing understanding of trace language inclusion.

Findings

Buffer-bounded game is decidable in polynomial time

Unbounded and bounded buffer game is highly undecidable

Conditions for Duplicator to win with unbounded buffers

Abstract

We consider simulation games played between Spoiler and Duplicator on two B\"uchi automata in which the choices made by Spoiler can be buffered by Duplicator in several buffers before she executes them on her structure. We show that the simulation games are useful to approximate the inclusion of trace closures of languages accepted by finite-state automata, which is known to be undecidable. We study the decidability and complexity and show that the game with bounded buffers can be decided in polynomial time, whereas the game with one unbounded and one bounded buffer is highly undecidable. We also show some sufficient conditions on the automata for Duplicator to win the game (with unbounded buffers).