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Regular Grammars as Effective Representations of Recognizable Sets of Series-Parallel Graphs

Authors Marius Bozga , Radu Iosif , Florian Zuleger

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LIPIcs.MFCS.2026.79.pdf
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ACM Subject Classification
  • Theory of computation → Grammars and context-free languages
Keywords
  • Series-parallel graphs
  • Regular grammars
  • Recognizability
  • Decision problems

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Abstract

Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism into a finite algebra. For SP-graphs, and more generally, for graphs of bounded tree-width, recognizability coincides with definability in Counting Monadic Second-Order (CMSO) logic. Despite this strong logical characterization, the conciseness and algorithmic effectiveness of syntactic representations of recognizable sets of SP (and bounded-tree-width) graphs remain poorly understood.
Building on previously introduced regular grammars for SP-graphs, we show that recognizable sets admit concise and effective syntactic representations. The main contribution is an improved construction of finite recognizer algebras whose size is singly-exponential in the size of a regular grammar, improving upon the previously known double-exponential bound. As a consequence, the problems of intersection and language inclusion for sets represented by regular grammars are shown to be EXPTIME-complete, thus improving on a previously known 2EXPTIME upper bound.

Cite As Get BibTex

Marius Bozga, Radu Iosif, and Florian Zuleger. Regular Grammars as Effective Representations of Recognizable Sets of Series-Parallel Graphs. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 79:1-79:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.79

Author Details

Marius Bozga
  • VERIMAG, CNRS, Université Grenoble Alpes, France
Radu Iosif
  • VERIMAG, CNRS, Université Grenoble Alpes, France
Florian Zuleger
  • Technische Universtität Wien, Austria
  • Technische Universtität München, Germany

Funding

Marius Bozga and Radu Iosif wish to acknowledge the support of the French National Research Agency project Non-Aggregative Resource COmpositions (NARCO) under grant number ANR-21-CE48-0011. Florian Zuleger wishes to acknowledge the support of the FWF project AUTOSARD: "Automated Sublinear Amortised Resource Analysis of Data Structures" No. P36623 and the project VASSAL: "Verification and Analysis for Safety and Security of Applications in Life" funded by the European Union under Horizon Europe WIDERA Coordination and Support Action/Grant Agreement No. 101160022.

Acknowledgements

All authors thank the anonymous reviewers for their insightful comments.

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