Counting Problems for Parikh Images

Authors Christoph Haase, Stefan Kiefer, Markus Lohrey

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Christoph Haase
Stefan Kiefer
Markus Lohrey

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Christoph Haase, Stefan Kiefer, and Markus Lohrey. Counting Problems for Parikh Images. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Given finite-state automata (or context-free grammars) A,B over the same alphabet and a Parikh vector p, we study the complexity of deciding whether the number of words in the language of A with Parikh image p is greater than the number of such words in the language of B. Recently, this problem turned out to be tightly related to the cost problem for weighted Markov chains. We classify the complexity according to whether A and B are deterministic, the size of the alphabet, and the encoding of p (binary or unary).
  • Parikh images
  • finite automata
  • counting problems


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