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Algorithmic games for full ground references.

Andrzej S Murawski1, Nikos Tzevelekos2

  • 11University of Warwick, Coventry, UK.

Formal Methods in System Design
|July 2, 2019
PubMed
Summary
This summary is machine-generated.

We fully classify decidable and undecidable cases for contextual equivalence in a finitary programming language with full ground storage. The simplest undecidable type identified is , impacting program analysis.

Keywords:
Automata over infinite alphabetsFull abstractionGame semanticsProgram equivalence

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Area of Science:

  • Theoretical Computer Science
  • Programming Language Theory
  • Formal Methods

Background:

  • Contextual equivalence is a fundamental program equivalence in programming language theory.
  • Finitary languages with ground storage present complex challenges for decidability analysis.
  • Previous work has explored decidability for simpler language features.

Purpose of the Study:

  • To provide a complete classification of decidable and undecidable instances of contextual equivalence.
  • To investigate these properties in a finitary ML-like language with comprehensive ground storage capabilities.
  • To identify the simplest type exhibiting undecidability.

Main Methods:

  • Integration of game semantics with automata-theoretic techniques for handling infinite alphabets.
  • Development and application of automata theory, specifically register pushdown automata.
  • Analysis of the emptiness problem for extended register pushdown automata with fresh-symbol generation.

Main Results:

  • A full classification of decidable and undecidable cases for contextual equivalence is established.
  • The simplest undecidable type in this language setting is identified as .
  • Decidability of the emptiness problem for register pushdown automata with fresh-symbol generation is proven.

Conclusions:

  • The study provides a precise boundary for decidability of contextual equivalence in expressive finitary languages.
  • The findings offer crucial insights for the design and analysis of programming languages with storage.
  • The technical advancements in automata theory contribute to solving problems with infinite alphabets.