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Undecidability in matrices over Laurent polynomials

Vesa Halava, Tero Harju
2004 Advances in Applied Mathematics  
This result follows from a representations of the integer weighted finite automata by matrices over Laurent polynomials.  ...  We show that it is undecidable for finite sets S of upper triangular (4 × 4)-matrices over Z[x, x −1 ] whether or not all elements in the semigroup generated by S have a nonzero constant term in some of  ...  We consider a generalization of finite automata where the transitions have integer weights.  ... 
doi:10.1016/j.aam.2004.04.002 fatcat:m33bmnfsnjeghaclct5ouf2q4e

Comparison of max-plus automata and joint spectral radius of tropical matrices [article]

Laure Daviaud, Pierre Guillon, Glenn Merlet
2017 arXiv   pre-print
Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S.  ...  This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata.  ...  Introduction Weighted automata were introduced by Schützenberger in [20] as a quantitative extension of nondeterministic finite automata.  ... 
arXiv:1612.02647v2 fatcat:mklscxtg5nc2fom56qh3yzxwxi

When is Containment Decidable for Probabilistic Automata?

Laure Daviaud, Marcin Jurdzinski, Ranko Lazic, Filip Mazowiecki, Guillermo A. Pérez, James Worrell, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We study it for probabilistic automata, where it is known to be undecidable in general. We restrict our study to the class of probabilistic automata with bounded ambiguity.  ...  There, we show decidability (subject to Schanuel's conjecture) when one of the automata is assumed to be unambiguous while the other one is allowed to be finitely ambiguous.  ...  In this paper, we refine the undecidability result by extending it to the class of linearly ambiguous automata. Theorem 1.  ... 
doi:10.4230/lipics.icalp.2018.121 dblp:conf/icalp/DaviaudJLMP018 fatcat:dhorpuaeibhb3ai23lpqsz2nde

Weighted automata on infinite words in the context of Attacker-Defender games [article]

Vesa Halava, Tero Harju, Reino Niskanen, Igor Potapov
2015 arXiv   pre-print
Firstly we prove a new language-theoretic result for weighted automata on infinite words and show its encoding into the framework of Attacker-Defender games.  ...  Secondly we use this novel concept to prove undecidability for checking existence of a winning strategy in several low-dimensional mathematical games including vector reachability games, word games and  ...  In [19] it was shown that the universality problem is undecidable for integer weighted finite automata on finite words by reduction from Post Correspondence Problem.  ... 
arXiv:1411.4796v3 fatcat:fz2erid2cvhipdkk3yzqjvfab4

Synchronizing weighted automata

Szabolcs Iván
2014 Electronic Proceedings in Theoretical Computer Science  
We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently, to finite sets of matrices in K^nxn.)  ...  We give sufficient conditions for the semiring K when the problems are PSPACE-complete and show several undecidability results as well, e.g. synchronizability is undecidable if 1 has infinite order in  ...  Acknowledgement The research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP-4.2.4.A/ 2-11/1-2012-0001 "National Excellence  ... 
doi:10.4204/eptcs.151.21 fatcat:wtoiozbmtbgpnk4syar4bacouu

Containment and Equivalence of Weighted Automata: Probabilistic and Max-Plus Cases [chapter]

Laure Daviaud
2020 Lecture Notes in Computer Science  
Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values.  ...  Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one.  ...  Introduction Weighted automata have been introduced by Schützenberger in 1961 in [37] as a quantitative generalisation of non deterministic finite-state automata.  ... 
doi:10.1007/978-3-030-40608-0_2 fatcat:gexpjfbjszfujmedra5va2ojsa

Page 5102 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
Summary: “It is shown that the universe problem L(s/’) = A* is undecidable for 4-state finite automata . with integer weight function y on its transitions.  ...  We also briefly discuss the case of simple matrix languages.” 2000g:68079 68Q45 Halava, Vesa (FIN-TURK-TC; Turku); Harju, Tero (FIN-TURK; Turku) Undecidability in integer weighted finite automata.  ... 

Weighted Automata on Infinite Words in the Context of Attacker-Defender Games [chapter]

Vesa Halava, Tero Harju, Reino Niskanen, Igor Potapov
2015 Lecture Notes in Computer Science  
Moreover, our result on integer weighted automata reveals a problem in a chain of previously claimed decidability results (in PSPACE) for several one-dimensional reachability games under different update  ...  In this paper we show undecidabillity of universality problem for weighted one counter automata over infinite words by direct reduction from any Infinite Post Correspondence Problem (ω PCP).  ...  First we show that universality problem for integer weighted automata on infinite words is undecidable.  ... 
doi:10.1007/978-3-319-20028-6_21 fatcat:fxtl4tw73fbfxa52m5iwuu2byq

Incompleteness Theorems, Large Cardinals, and Automata Over Finite Words

Olivier Finkel
2019 International Journal of Foundations of Computer Science  
Moreover we get some independence results for weighted automata and for some related finitely generated subsemigroups of the set Z 3×3 of 3-3 matrices with integer entries.  ...  In particular, we prove independence results for languages of finite words generated by contextfree grammars, or accepted by 2-tape or 1-counter automata.  ...  We also prove some independence results for weighted automata, via some independence results for finitely generated matrix subsemigroups of Z 3×3 .  ... 
doi:10.1142/s012905411950014x fatcat:bvcu7lvnfngppglbfj3xzboslm

Page 2841 of Mathematical Reviews Vol. , Issue 89E [page]

1989 Mathematical Reviews  
; it is undecidable whether all (finite) configurations of a CA evolve to the quiescent configuration; it is undecidable whether a CA is in Class 2; it is undecidable whether a CA is in Class 3.  ...  2841 89e:68094 68Q80 03D05 68Q45 Culik, Karel, IT (1-SC) On invertible cellular automata. Complex Systems 1 (1987), no. 6, 1035-1044. Let S be a finite set of symbols and d be a positive integer.  ... 

When is Containment Decidable for Probabilistic Automata? [article]

Laure Daviaud, Marcin Jurdziński, Ranko Lazić, Filip Mazowiecki, Guillermo A. Pérez, James Worrell
2020 arXiv   pre-print
We complement this positive result by showing that the emptiness problem remains undecidable even when restricted to automata of linear ambiguity. We then turn to finitely ambiguous automata.  ...  It is well known that both problems are undecidable. In this paper we provide a more refined view of these problems in terms of the degree of ambiguity of probabilistic automata.  ...  Mazowiecki, by the French National Research Agency (ANR) in the frame of the "Investments for the future" Programme IdEx Bordeaux (ANR-10-IDEX-03-02); G. A. Pérez, by an F.R.S.  ... 
arXiv:1804.09077v4 fatcat:ds5azb7dozfepj6iovjg6wjoxm

What's Decidable about Weighted Automata? [chapter]

Shaull Almagor, Udi Boker, Orna Kupferman
2011 Lecture Notes in Computer Science  
Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of containment vs. universality and the front of the ∪ {∞} vs. the ¡ ∪ {∞} domains  ...  Weighted Automata With Integer Weights In this section we show that the universality problem, and therefore also the containment problem, are undecidable for WFAs with weights in ¤ .  ...  This is the case with Boolean automata, in which they are both PSPACE-complete [14] , as well as with weighted automata over integer weights, for which the previous section shows undecidability.  ... 
doi:10.1007/978-3-642-24372-1_37 fatcat:wul25bahdrauxgyqhjqozviiwu

On model-checking timed automata with stopwatch observers

Thomas Brihaye, Véronique Bruyère, Jean-François Raskin
2006 Information and Computation  
In this paper, we study the model-checking problem for weighted timed automata and the weighted CTL logic; we also study the finiteness of bisimulations of weighted timed automata.  ...  the dense case, for a slight restriction of the weighted CTL Logic, (iii) the precise frontier between finite and infinite bisimulations in the dense case for the subclass of stopwatch automata.  ...  There exist weighted timed automata with 1 clock variable x and 1 cost variable z such thatż = d 1 ,ż = d 2 , with d 1 , d 2 > 0 two integer constants, for which no finite bisimulation exists [13] (see  ... 
doi:10.1016/j.ic.2005.12.001 fatcat:qdmb5j2yzfg7rc4q2er3busaci

Probabilistic automata of bounded ambiguity

Nathanaël Fijalkow, Cristian Riveros, James Worrell
2020 Information and Computation  
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities.  ...  The known undecidability proofs exploits infinite ambiguity and so we focus on the case of finitely ambiguous probabilistic automata.  ...  Conclusions We have initiated the study of the computational complexity of analysing finitely ambiguous probabilistic automata.  ... 
doi:10.1016/j.ic.2020.104648 fatcat:d2d2ijbuobazrl7dfyutrs7jbu

Page 5388 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Summary: “The surjectivity problem for 2D cellular automata was proved undecidable in 1989 by Jarkko Kari. The proof consists in a reduction of a problem concerning finite tilings to this problem.  ...  In this paper, we provide another characterization of this family using asynchronous cellular automata (which carry the most intuitive idea of finite state concurrent machines).  ... 
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