| Title: | Pumping-like results for copyless cost register automata and polynomially ambiguous weighted automata |
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| Authors: | ID Mazowiecki, Filip (Author)
ID Puch, Antoni (Author)
ID Smertnig, Daniel (Author) |
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| Files: |  PDF - Presentation file, download (1,21 MB)
MD5: 11736C788E7ADEBF29895D958388B00C
 URL - Source URL, visit https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.67
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| Language: | English |
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| Typology: | 1.08 - Published Scientific Conference Contribution |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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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 NC$^2$ 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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| Keywords: | weighted automata, cost register automata, ambiguity, linear recurrence sequences, equivalence problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 67:1-67:21 |
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| PID: | 20.500.12556/DiRROS-29429  |
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| UDC: | 004:511 |
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| ISSN on article: | 1868-8969 |
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| DOI: | 10.4230/LIPIcs.STACS.2026.67 |
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| COBISS.SI-ID: | 278513155 |
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| Note: |
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| Publication date in DiRROS: | 18.05.2026 |
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| Views: | 27 |
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| Downloads: | 17 |
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