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Probabilistic and Nondeterministic Unary Automata [chapter]

Gregor Gramlich
2003 Lecture Notes in Computer Science  
We investigate unary regular languages and compare deterministic finite automata (DFA's), nondeterministic finite automata (NFA's) and probabilistic finite automata (PFA's) with respect to their size.  ...  Thus we show that for the model of probabilistic automata with a constant error bound, there is only a polynomial blowup for cyclic languages.  ...  This result offers some clues about the composition of the (ultimate) period of a unary language which also apply to probabilistic finite automata which we define as follows.  ... 
doi:10.1007/978-3-540-45138-9_40 fatcat:xfleavb24re25csdev233om5te

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Carlo Mereghetti, Beatrice Palano, Giovanni Pighizzini
2001 RAIRO - Theoretical Informatics and Applications  
These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.  ...  In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is p α 1 1 + p  ...  Further results concerning acceptance of unary languages are proved in [14] for two-way nondeterministic automata and in [17] for one-way probabilistic automata.  ... 
doi:10.1051/ita:2001106 fatcat:zjw2mm2dizdqxpomz64jnj6vlm

Normal forms for unary probabilistic automata

Maria Paola Bianchi, Giovanni Pighizzini
2012 RAIRO - Theoretical Informatics and Applications  
In the nondeterministic case there are trivial simulations between Chrobak normal form and cyclic normal form, preserving the total number of states in the automata and in their cycles.  ...  While in the nondeterministic case a unary automaton can be simulated by an automaton in Chrobak normal form without increasing the number of the states in the cycles, we show that in the probabilistic  ...  The authors would like to thank the reviewers for their careful work and stimulating comments. In particular, the example of the language Lp presented in the Conclusion was suggested by a referee.  ... 
doi:10.1051/ita/2012017 fatcat:n5dz6omsyfdphp357bazfmmgqi

Convex Language Semantics for Nondeterministic Probabilistic Automata [article]

Gerco van Heerdt, Justin Hsu, Joël Ouaknine, Alexandra Silva
2018 arXiv   pre-print
We explore language semantics for automata combining probabilistic and nondeterministic behavior.  ...  For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking language equivalence is undecidable by reduction  ...  In this paper we study nondeterministic probabilistic automata (NPAs) and propose a novel probabilistic language semantics.  ... 
arXiv:1805.11550v1 fatcat:5e53ifggtzbvvlbfhdvukis5gu

Page 2872 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
These results are settled within a survey on unary automata aiming to compare the descriptional power of determin- istic, nondeterministic, probabilistic and quantum paradigms.” 2003d:68068 68Q05 68Q10  ...  , probabilistic and quantum finite automata.  ... 

Unary languages recognized by two-way one-counter automata [article]

Marzio De Biasi, Abuzer Yakaryilmaz
2014 arXiv   pre-print
By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear--space Turing machines.  ...  Finally, we compare unary 2D1CAs with two--counter machines and provide some insights about the limits of their computational power.  ...  We thank Alexander Okhotin, Holger Petersen, and Klaus Reinhardt for their answers to our questions on the subject matter of this paper.  ... 
arXiv:1311.0849v2 fatcat:4mmokdl2prej3h4g2xwo23uy5q

Unary Languages Recognized by Two-Way One-Counter Automata [chapter]

Marzio De Biasi, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear-space Turing machines.  ...  Finally, we compare unary 2D1CAs with two-counter machines and provide some insights about the limits of their computational power.  ...  We thank Alexander Okhotin, Holger Petersen, and Klaus Reinhardt for their answers to our questions on the subject matter of this paper.  ... 
doi:10.1007/978-3-319-08846-4_11 fatcat:xk7qy27eorf7jlsh5tlu5nba3m

Tight bounds for the space complexity of nonregular language recognition by real-time machines [article]

Abuzer Yakaryilmaz, A. C. Cem Say
2013 arXiv   pre-print
We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs.  ...  It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.  ...  Bruda, Giovanni Pighizzini, Juraj Hromkovič, and Rūsiņš Freivalds for their helpful answers to our questions.  ... 
arXiv:1108.2613v2 fatcat:j5klwx3auzdppmluq3wtgp6vdu

The Minimum Amount of Useful Space: New Results and New Directions [chapter]

Klaus Reinhardt, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
We consider minimal space requirements when using memory with restricted access policy (pushdown -hence giving pushdown automata (PDAs), and counter -hence giving counter automata (CAs)) in connection  ...  alternating CAs within weak log n space, (iii) there exist nonregular languages accepted by two-way DPADs within strong log log n space, and, (iv) there exist unary nonregular languages accepted by two-way  ...  our questions on the subject matter of this paper, and, the anonymous reviewers for their very helpful comments (based on which we rewrote the abstract and made many corrections within the text).  ... 
doi:10.1007/978-3-319-09698-8_28 fatcat:ht5j2x4qrjamrba4nrct4fi7dq

Size Complexity of Two-Way Finite Automata [chapter]

Christos A. Kapoutsis
2009 Lecture Notes in Computer Science  
This is a talk on the size complexity of two-way finite automata.  ...  We add little to what is already known-only exposition, terminology, and questions.  ...  Another natural restriction one can focus on is that of unary automata. For each class C in Fig. 3b , one can consider the class unary-C that is defined identically to C but for unary automata.  ... 
doi:10.1007/978-3-642-02737-6_4 fatcat:ousdbu3jgfctnofd464zsmpo3m

Complementing Two-Way Finite Automata [chapter]

Viliam Geffert, Carlo Mereghetti, Giovanni Pighizzini
2005 Lecture Notes in Computer Science  
This allows the simulation of unary 2nfa's by probabilistic Las Vegas two-way automata with O(n 8 ) states.  ...  We study the relationship between the sizes of two-way finite automata accepting a language and its complement.  ...  Acknowledgment The authors thank an anonymous referee for her/his helpful comments and remarks.  ... 
doi:10.1007/11505877_23 fatcat:2drvedou2ff5rpljrhya44dtri

Complementing two-way finite automata

Viliam Geffert, Carlo Mereghetti, Giovanni Pighizzini
2007 Information and Computation  
This allows the simulation of unary 2nfa's by probabilistic Las Vegas two-way automata with O(n 8 ) states.  ...  We study the relationship between the sizes of two-way finite automata accepting a language and its complement.  ...  Acknowledgment The authors thank an anonymous referee for her/his helpful comments and remarks.  ... 
doi:10.1016/j.ic.2007.01.008 fatcat:q5hb2j2q5jgknmajmxaat3luf4

Classical Automata on Promise Problems

Viliam Geffert, Abuzer Yakaryilmaz
2015 Discrete Mathematics & Theoretical Computer Science  
By comparing this with the corresponding state complexity of alternating machines, we then get a tight exponential gap between two-way nondeterministic and one-way alternating automata solving unary promise  ...  Second, despite of the existing quadratic gap between Las Vegas realtime probabilistic automata and one-way deterministic automata for language recognition, we show that, by turning to promise problems  ...  First, let us show that the classes of promise problems solvable by deterministic, nondeterministic, alternating, and Las Vegas probabilistic finite automata are identical.  ... 
doi:10.46298/dmtcs.2138 fatcat:u6wynlc34nbp3dxyjchyarxw5i

Classical Automata on Promise Problems [chapter]

Viliam Geffert, Abuzer Yakaryılmaz
2014 Lecture Notes in Computer Science  
By comparing this with the corresponding state complexity of alternating machines, we then get a tight exponential gap between two-way nondeterministic and one-way alternating automata solving unary promise  ...  Second, despite of the existing quadratic gap between Las Vegas realtime probabilistic automata and oneway deterministic automata for language recognition, we show that, by turning to promise problems,  ...  First, we show that the classes of promise problems solvable by deterministic, nondeterministic, alternating, and Las Vegas probabilistic finite automata are identical.  ... 
doi:10.1007/978-3-319-09704-6_12 fatcat:n6tnt6spl5fwfabiih5i5hp454

Decision problems on unary probabilistic and quantum automata [article]

Mika Hirvensalo, Abuzer Yakaryılmaz
2016 arXiv   pre-print
We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem's and positivity problems.  ...  It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable.  ...  Stochastic versions (probabilistic finite automata (PFAs)) were introduced in [17] , and their properties were extensively studied in [16] .  ... 
arXiv:1610.01397v1 fatcat:ewpowktn7zhjdcqlrq5t2in6v4
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