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Weighted GKAT: Completeness and Complexity

Authors Spencer Van Koevering , Wojciech Różowski , Alexandra Silva

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ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Weighted Programming
  • Automata
  • Axiomatization
  • Decision Procedure

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Abstract

We propose Weighted Guarded Kleene Algebra with Tests (wGKAT), an uninterpreted weighted programming language equipped with branching, conditionals, and loops. We provide an operational semantics for wGKAT using a variant of weighted automata and introduce a sound and complete axiomatization. We also provide a polynomial time decision procedure for bisimulation equivalence.

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Spencer Van Koevering, Wojciech Różowski, and Alexandra Silva. Weighted GKAT: Completeness and Complexity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 172:1-172:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.172

Author Details

Spencer Van Koevering
  • Cornell University, Ithaca, NY, USA
Wojciech Różowski
  • University College London, UK
Alexandra Silva
  • Cornell University, Ithaca, NY, USA

Funding

  • Van Koevering, Spencer: Partially supported by a Cornell Bowers CIS Deans Excellence Fellowship.
  • Różowski, Wojciech: Partially supported by ERC grant Autoprobe (grant agreement 101002697).
  • Silva, Alexandra: Partially supported by ONR grant N68335-22-C-0411, ERC grant 101002697, and a Royal Society Wolfson fellowship.

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