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Documents authored by Draghici, Andrei

Document
DOI: 10.4230/LIPIcs.CSL.2025.20
Boundedness of Cost Register Automata over the Integer Min-Plus Semiring

Authors: Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Cost register automata (CRAs) are deterministic automata with registers taking values from a fixed semiring. A CRA computes a function from words to values from this semiring. CRAs are tightly related to well-studied weighted automata. Given a CRA, the boundedness problem asks if there exists a natural number N such that for every word, the value of the CRA on this word does not exceed N. This problem is known to be undecidable for the class of linear CRAs over the integer min-plus semiring (ℤ∪{+∞}, min, +), but very little is known about its subclasses. In this paper, we study boundedness of copyless linear CRAs with resets over the integer min-plus semiring. We show that it is decidable for such CRAs with at most two registers. More specifically, we show that it is, respectively, NL-complete and in coNP if the numbers in the input are presented in unary and binary. We also provide complexity results for two classes with an arbitrary number of registers. Namely, we show that for CRAs that use the minimum operation only in the output function, boundedness is PSPACE-complete if transferring values to other registers is allowed, and is coNP-complete otherwise. Finally, for each f_i in the hierarchy of fast-growing functions, we provide a stateless CRA with i registers whose output exceeds N only on runs longer than f_i(N). Our construction yields a non-elementary lower bound already for four registers.
Cite as

Andrei Draghici, Radosław Piórkowski, and Andrew Ryzhikov. Boundedness of Cost Register Automata over the Integer Min-Plus Semiring. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{draghici_et_al:LIPIcs.CSL.2025.20,
  author =	{Draghici, Andrei and Pi\'{o}rkowski, Rados{\l}aw and Ryzhikov, Andrew},
  title =	{{Boundedness of Cost Register Automata over the Integer Min-Plus Semiring}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{20:1--20:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.20},
  URN =		{urn:nbn:de:0030-drops-227775},
  doi =		{10.4230/LIPIcs.CSL.2025.20},
  annote =	{Keywords: cost register automata, boundedness, decidability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.29
Semënov Arithmetic, Affine {VASS}, and String Constraints

Authors: Andrei Draghici, Christoph Haase, and Florin Manea

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
We study extensions of Semënov arithmetic, the first-order theory of the structure ⟨ℕ,+,2^x⟩. It is well-known that this theory becomes undecidable when extended with regular predicates over tuples of number strings, such as the Büchi V₂-predicate. We therefore restrict ourselves to the existential theory of Semënov arithmetic and show that this theory is decidable in EXPSPACE when extended with arbitrary regular predicates over tuples of number strings. Our approach relies on a reduction to the language emptiness problem for a restricted class of affine vector addition systems with states, which we show decidable in EXPSPACE. As an application of our result, we settle an open problem from the literature and show decidability of a class of string constraints involving length constraints.
Cite as

Andrei Draghici, Christoph Haase, and Florin Manea. Semënov Arithmetic, Affine {VASS}, and String Constraints. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 29:1-29:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{draghici_et_al:LIPIcs.STACS.2024.29,
  author =	{Draghici, Andrei and Haase, Christoph and Manea, Florin},
  title =	{{Sem\"{e}nov Arithmetic, Affine \{VASS\}, and String Constraints}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{29:1--29:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.29},
  URN =		{urn:nbn:de:0030-drops-197393},
  doi =		{10.4230/LIPIcs.STACS.2024.29},
  annote =	{Keywords: arithmetic theories, B\"{u}chi arithmetic, exponentiation, vector addition systems with states, string constraints}
}
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