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Finite automata and unary languages

Marek Chrobak
1986 Theoretical Computer Science  
We also show that O(n 2) states are sufficient and necessary to simulate an n-state lnfa recognizing a unary language by a 2dfa. to the next-state function.  ...  We prove that O(e " t' /gT-~g~") states are sufficient to simulate an n-state lnfa recognizing a unary language by a ldfa. The lower bound is the same.  ...  Rytter and B. Chlebus for many discussions on the problems presented in this paper. W. Rytter has also discovered references [7, 15, 16, 29] . I am especially grateful to Prof. A.  ... 
doi:10.1016/0304-3975(86)90142-8 fatcat:tsjp7dzplzg4fnyno2xtkhvufy

Errata to: "Finite Automata and Unary Languages"

Marek Chrobak
2003 Theoretical Computer Science  
Acknowledgements I would like to thank Je Shallit for pointing out this error and suggesting the above correction.  ...  In [1] , I presented several results on the state complexity of di erent types of ÿnite automata for unary languages.  ...  We also show that O(n 2 ) states are su cient and necessary to simulate an n-state 1 nfa recognizing a unary language by a 2 dfa.  ... 
doi:10.1016/s0304-3975(03)00136-1 fatcat:l6gw5uqpujfxnbpzv5yqyujqti


2009 International Journal of Foundations of Computer Science  
Deterministic pushdown automata and unary languages.  ...  Since each unary context-free language is regular, these devices are equivalent to finite automata.  ...  Since each unary context-free language is regular, these devices are equivalent to finite automata.  ... 
doi:10.1142/s0129054109006784 fatcat:dfwazoy7tjf3fcvneg5shyx2de

Size of Unary One-Way Multi-head Finite Automata [chapter]

Martin Kutrib, Andreas Malcher, Matthias Wendlandt
2013 Lecture Notes in Computer Science  
On the one hand, many automata models such as one-way finite automata, two-way finite automata, pushdown automata, or context-free grammars for unary languages are investigated and compared to each other  ...  Here, we consider deterministic one-way multi-head finite automata accepting unary languages.  ... 
doi:10.1007/978-3-642-39310-5_15 fatcat:odbv4r7jtbbknidti5wpwjbolq

Limited automata and unary languages

Giovanni Pighizzini, Luca Prigioniero
2019 Information and Computation  
When d = 1 these models characterize regular languages. An exponential gap between the size of limited automata accepting unary languages and the size of equivalent finite automata is proved.  ...  Furthermore, despite the exponential gap between the sizes of limited automata and of equivalent unary finite automata, there are unary regular languages for which d-limited automata cannot be significantly  ...  Unary Grammars versus Limited Automata In Section 3 we proved an exponential gap between unary 1-las and finite automata. A similar gap was obtained between unary cfgs and finite automata [9] .  ... 
doi:10.1016/j.ic.2019.01.002 fatcat:l4ts3gyqbzfmbh6jjsdz52xb3u

Descriptional and computational complexity of finite automata—A survey

Markus Holzer, Martin Kutrib
2011 Information and Computation  
Descriptional and Computational Complexity of Finite Automata, Proc. 3rd Int. Conf. Language M. Holzer, M.  ...  In truth there is much more to the regular languages, DFAs, NFAs, etc., than one can summarize here. For a recent survey on finite automata we refer to [87] and [38].  ...  These completeness results even hold for finite automata accepting languages over a singleton, i.e., unary languages.  ... 
doi:10.1016/j.ic.2010.11.013 fatcat:qisoh4k6snfuvbgowrj5bllsli

On the descriptional power of heads, counters, and pebbles

Martin Kutrib
2005 Theoretical Computer Science  
Here we present huge lower bounds for the unary tradeoffs between non-deterministic finite automata and any k-DHA, k 2.  ...  Such non-recursive trade-offs are also shown between any k-DHA, k 1, and DSPACE(log) = multi-DHA. We also address the particular case of unary languages.  ...  The rest of the section is devoted to huge unary lower bounds for the trade-off between finite automata with k heads and non-deterministic finite automata.  ... 
doi:10.1016/j.tcs.2004.04.013 fatcat:u2nr4t3twzcubmfoyhfqcn7iwa

Page 2665 of Mathematical Reviews Vol. , Issue 2001D [page]

2001 Mathematical Reviews  
simulations and unary languages.  ...  Next, we prove a tight lower bound on the number of states of two-way deterministic, nondeterministic, and quasi sweeping automata accepting unary languages.  ... 

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

Carlo Mereghetti, Beatrice Palano, Giovanni Pighizzini
2001 RAIRO - Theoretical Informatics and Applications  
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  ...  Moreover, we exhibit one-way quantum finite automata that, for any m, accept Lm with isolated cut point and only two states.  ...  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

Restricted deterministic Watson-Crick automata [article]

Kingshuk Chatterjee, Kumar Sankar Ray
2016 arXiv   pre-print
We examine the computational power of the restricted model with respect to L being in different language classes such as regular, unary regular, finite, context free and context sensitive.  ...  accepted by restricted deterministic Watson-Crick automata with L in unary regular languages is a proper subset of context free languages.  ...  As L=a * is a unary regular language therefore regular languages is a subset of the set of all languages accepted by restricted deterministic Watson-Crick automata where L is a unary regular language.  ... 
arXiv:1602.05721v1 fatcat:s4szypboqjfvvgjwu75p2orx34

Parikh's Theorem and Descriptional Complexity [chapter]

Giovanna J. Lavado, Giovanni Pighizzini
2012 Lecture Notes in Computer Science  
) Lower bound: 2 s 2 (from the unary case) Problem Given a CFG G compare the size of G with the sizes of finite automata accepting languages that are Parikh equivalent to L(G ) Deterministic automata (  ...  O(4 s ) [Esparza&Ganty&Kiefer&Luttenberger '11] Lower bound: Ω(2 s ) Upper and Lower Bounds Problem Given a CFG G compare the size of G with the sizes of finite automata accepting languages that are Parikh  ...  The use of nonunary variables is very restricted: If S ⇒ α then α contains ≤ m − 1 nonunary variables Hence a finite control of size O(h m−1 ) can keep track of them First Contribution: Proof Outline Σ  ... 
doi:10.1007/978-3-642-27660-6_30 fatcat:fjxchgsoljgnjbb3nehc6ydsgq

Photonic realization of a quantum finite automaton

Carlo Mereghetti, Beatrice Palano, Simone Cialdi, Valeria Vento, Matteo G. A. Paris, Stefano Olivares
2020 Physical Review Research  
We describe a physical implementation of a quantum finite automaton recognizing a well known family of periodic languages.  ...  The realization exploits the polarization degree of freedom of single photons and their manipulation through linear optical elements.  ...  Clearly, unary oneway finite automata accept unary languages L ⊆ a * .  ... 
doi:10.1103/physrevresearch.2.013089 fatcat:yw7ehwsw45b2dny5olmqqvuwku

Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent Deterministic Automata [chapter]

Giovanna J. Lavado, Giovanni Pighizzini, Shinnosuke Seki
2012 Lecture Notes in Computer Science  
We investigate the conversion of nondeterministic finite automata and context-free grammars into Parikh equivalent deterministic finite automata, from a descriptional complexity point of view.  ...  Introduction It is well-known that the state cost of the conversion of nondeterministic finite automata (NFAs) into equivalent deterministic finite automata (DFAs) is exponential: using the classical subset  ...  which are used to specify languages as, for instance, grammars and automata.  ... 
doi:10.1007/978-3-642-31653-1_26 fatcat:xxrlca7pjjhujglpainm3duwhq

Page 7067 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
This paper studies the size, or the descriptive complexity, of context-free grammars, finite automata, and (auxiliary) pushdown automata, from the point of view of how complex are unary languages, i.e.  ...  ; Waterloo, ON) Unary context-free grammars and pushdown automata, descriptional complexity and auxiliary space lower bounds.  ... 

Unambiguity in Timed Regular Languages: Automata and Logics [chapter]

Paritosh K. Pandya, Simoni S. Shah
2010 Lecture Notes in Computer Science  
A subclass of the two-way deterministic timed automata (2DTA) of Alur and Henzinger, called partially-ordered two-way deterministic automata (po2DTA) are examined and we call the languages accepted by  ...  We propose a deterministic and unary variant of MTL called DUMTL and show that DUMTL formulae can be reduced to language equivalent po2DTA in polynomial time, giving NPcomplete satisfiability for the logic  ...  The connection between temporal logics and finite automata provides the key to algorithmic analysis and reasoning about logical properties of reactive systems.  ... 
doi:10.1007/978-3-642-15297-9_14 fatcat:dqjhqbzobrbu5iz7zcr3mh6uba
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