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Decision Problems for Restricted Variants of Two-Dimensional Automata [article]

Taylor J. Smith, Kai Salomaa
2019 arXiv   pre-print
We show that the language equivalence problem for two-way deterministic two-dimensional automata is decidable, while both the equivalence and universality problems for two-way nondeterministic two-dimensional  ...  We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is NP-complete, and is in P for general-alphabet two-way nondeterministic two-dimensional automata  ...  Decision problems for two-way two-dimensional automata have not been considered much in the literature.  ... 
arXiv:1904.11100v1 fatcat:l7b66z2ogngctafvsefwyzmgbq

Conjugacy of one-dimensional one-sided cellular automata is undecidable [article]

Joonatan Jalonen, Jarkko Kari
2017 arXiv   pre-print
following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  We will reduce the decision problem of Theorem 1 to this problem, which will prove our claim.  ... 
arXiv:1710.08111v1 fatcat:cdizyyuryfaoriboabubkmshsm

Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable [chapter]

Joonatan Jalonen, Jarkko Kari
2017 Lecture Notes in Computer Science  
following decision problems are undecidable: Given two one-dimensional one-sided cellular automata F and G over a full shift: Are F and G conjugate?  ...  It also immediately follows that these results hold for one-dimensional two-sided cellular automata.  ...  We will reduce the decision problem of Theorem 1 to this problem, which will prove our claim.  ... 
doi:10.1007/978-3-319-73117-9_16 fatcat:afsytbockbbbfhjd6hirucfhnq

Parameterized Weighted Containment

Guy Avni, Orna Kupferman
2014 ACM Transactions on Computational Logic  
We are still able to study variants of the problems, where containment is replaced by simulation.  ...  We argue that both problems are useful in stepwise design of weighted systems as well as approximated minimization of weighted automata.  ...  We thank Nati Linial for the helpful discussions and pointers. References  ... 
doi:10.1145/2665076 fatcat:s36qetud3fa2zmq2taousxjqz4

Parameterized Weighted Containment [chapter]

Guy Avni, Orna Kupferman
2013 Lecture Notes in Computer Science  
We are still able to study variants of the problems, where containment is replaced by simulation.  ...  We argue that both problems are useful in stepwise design of weighted systems as well as approximated minimization of weighted automata.  ...  Acknowledgments We thank Nati Linial for the helpful discussions and pointers. References  ... 
doi:10.1007/978-3-642-37075-5_24 fatcat:iw3otqyfvzezzaewhqyfpmy3qa

Page 812 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
Thus, different variants of the parameter-parsing mechanisms arise: call-by-value and two different types of call-by-name: call-time-choice and run-time-choice.  ...  An algorithm A for the solution of a basic problem of pattern recognition (identification) is represented in the form of successive application of the pattern recognition operator A’ and the decision rule  ... 

Decision Problems for Linear Recurrence Sequences [chapter]

Joël Ouaknine, James Worrell
2012 Lecture Notes in Computer Science  
In this paper, we survey the state of the art concerning certain fundamental decision problems for linear recurrence sequences, namely the Skolem Problem (does the sequence have a zero?)  ...  Linear recurrence sequences permeate a vast number of areas of mathematics and computer science.  ...  The purported proof attempts to reduce non-universality for two-letter automata to the Skolem Problem.  ... 
doi:10.1007/978-3-642-33512-9_3 fatcat:r5cwd5mazvgmbbsle3p6lps2xq

Decision Problems for Linear Recurrence Sequences [chapter]

Joël Ouaknine
2013 Lecture Notes in Computer Science  
In this paper, we survey the state of the art concerning certain fundamental decision problems for linear recurrence sequences, namely the Skolem Problem (does the sequence have a zero?)  ...  Linear recurrence sequences permeate a vast number of areas of mathematics and computer science.  ...  The purported proof attempts to reduce non-universality for two-letter automata to the Skolem Problem.  ... 
doi:10.1007/978-3-642-40164-0_2 fatcat:xrab2jhrgfhang4a2mnatluvgu

Hybrid automata with finite bisimulations [chapter]

Thomas A. Henzinger
1995 Lecture Notes in Computer Science  
The analysis, veri cation, and control of hybrid automata with nite bisimulations can be reduced to nite-state problems.  ...  For example, we prove that if two h ybrid automata have nite bisimulations, and both can be calibrated to a common time scale, then their product also has a nite bisimulation.  ...  We also thank Oded Maler and Howard Wong-Toi for valuable comments.  ... 
doi:10.1007/3-540-60084-1_85 fatcat:rgq4jxudqraqddowj7xh4p765e

Page 8287 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
Summary (translated from the Russian): “We consider the problem of traversing spatial labyrinths by automata.  ...  On traversing labyrinths by automata in n-dimensional space. (Russian. Russian summary) Diskret. Mat. 12 (2000), no. 4, 121-137; translation in Discrete Math. Appl. 10 (2000), no. 6, 597-612.  ... 

Complexity-Theoretic Aspects of Expanding Cellular Automata [article]

Augusto Modanese
2019 arXiv   pre-print
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint.  ...  The respective polynomial-time complexity class is shown to coincide with <_tt^p(NP), that is, the class of decision problems polynomial-time truth-table reducible to problems in NP.  ...  Acknowledgments The author would like to thank Thomas Worsch for his mentoring, encouragement, and support during the writing of this paper.  ... 
arXiv:1902.05487v2 fatcat:bj4bwhzx65dqdhn37v3h2hmjeq

Characterizations of 1-Way Quantum Finite Automata

Alex Brodsky, Nicholas Pippenger
2002 SIAM journal on computing (Print)  
In this paper we study two different models of 1-way quantum finite automata.  ...  We characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group.  ...  Reversible Finite Automata Unitary operations are reversible, thus QFAs bear strong resemblance to various variants of reversible finite automata.  ... 
doi:10.1137/s0097539799353443 fatcat:uizartdqxzblbbg64uxb5hnx2y

Extended Models of Finite Automata [article]

Özlem Salehi
2019 arXiv   pre-print
We examine the effect of various parameters on the language recognition power. We establish a link between the decision problems of matrix semigroups and the corresponding automata.  ...  In this thesis, we focus on two such models, namely the finite automata over groups and the homing vector automata.  ...  Undecidability of the Decision Problems for SL(4, Z)-automata In this section we are going to prove undecidability results for the emptiness and universe problems of SL(4, Z)-automata.  ... 
arXiv:1912.11699v1 fatcat:umb4afgbhzatratlrleuvnrmmm

Modeling of Microstructure Evolution during Deformation Processes by Cellular Automata—Boundary Conditions and Space Reorganization Aspects

Łukasz Łach
2021 Materials  
A set of decision rules for selecting space reorganization options taking into account the changes of CA shape and sizes is also presented.  ...  Cellular automata (CA) are efficient and effective numerical tools for modeling various phenomena and processes, e.g., microstructure evolution in plastic working processes.  ...  Conflicts of Interest: The author declares no conflict of interest.  ... 
doi:10.3390/ma14061377 pmid:33809120 fatcat:ilev3prdanfgfg3ov62smeswui

Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States [chapter]

Martin Fränzle
1999 Lecture Notes in Computer Science  
In the case of so-called linear hybrid automata this formalization supports semi-decision procedures for state reachability, yet no decision procedures due to inherent undecidability 4].  ...  Hybrid automata have been introduced in both control engineering and computer science as a formal model for the dynamics of hybrid discrete-continuous systems.  ...  A semi-decision procedure for A being unsafe has already been devised in Sect. 2. Hence, it remains to establish a semi-decision procedure for safety of robust automata.  ... 
doi:10.1007/3-540-48168-0_10 fatcat:nnklkyc2cvbgrcrmc4ee7yggqe
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