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Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata

Authors Filip Mazowiecki , Antoni Puch , Daniel Smertnig

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LIPIcs.STACS.2026.67.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Quantitative automata
Keywords
  • weighted automata
  • cost register automata
  • ambiguity
  • linear recurrence sequences
  • equivalence problem

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Abstract

In this work we consider two rich subclasses of weighted automata over fields: polynomially ambiguous weighted automata and copyless cost register automata. Primarily we are interested in understanding their expressiveness power. Over the field of rationals and 1-letter alphabets, it is known that the two classes coincide; they are equivalent to linear recurrence sequences (LRS) whose exponential bases are roots of rationals. We develop a tool we call Pumping Sequence Families, which, by exploiting the simple single-letter behaviour of the models, yields two pumping-like results over arbitrary fields with unrestricted alphabets, one for each class. As a corollary of these results, we present examples proving that the two classes become incomparable over the field of rationals with unrestricted alphabets.
We complement the results by analysing the zeroness and equivalence problems. For weighted automata (even unrestricted) these problems are well understood: there are polynomial time, and even NC² algorithms. For copyless cost register automata we show that the two problems are PSpace-complete, where the difficulty is to show the lower bound.

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Filip Mazowiecki, Antoni Puch, and Daniel Smertnig. Pumping-Like Results for Copyless Cost Register Automata and Polynomially Ambiguous Weighted Automata. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 67:1-67:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.STACS.2026.67

Author Details

Filip Mazowiecki
  • University of Warsaw, Poland
Antoni Puch
  • University of Warsaw, Poland
Daniel Smertnig
  • University of Ljubljana and Institute of Mathematics, Physics, and Mechanics (IMFM), Slovenia

Funding

  • Mazowiecki, Filip: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00230.
  • Puch, Antoni: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00230.
  • Smertnig, Daniel: Supported by the Slovenian Research and Innovation Agency (ARIS) program P1-0288 and grant J1-60025.

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