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Finite automata and unary languages

1986
*
Theoretical Computer Science
*

We also show that O(n 2) states are sufficient

doi:10.1016/0304-3975(86)90142-8
fatcat:tsjp7dzplzg4fnyno2xtkhvufy
*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. ...##
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Errata to: "Finite Automata and Unary Languages"

2003
*
Theoretical Computer Science
*

Acknowledgements I would like to thank Je Shallit for pointing out this error

doi:10.1016/s0304-3975(03)00136-1
fatcat:l6gw5uqpujfxnbpzv5yqyujqti
*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. ...##
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DETERMINISTIC PUSHDOWN AUTOMATA AND UNARY LANGUAGES

2009
*
International Journal of Foundations of Computer Science
*

Deterministic pushdown

doi:10.1142/s0129054109006784
fatcat:dfwazoy7tjf3fcvneg5shyx2de
*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*. ...##
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Size of Unary One-Way Multi-head Finite Automata
[chapter]

2013
*
Lecture Notes in Computer Science
*

On the one hand, many

doi:10.1007/978-3-642-39310-5_15
fatcat:odbv4r7jtbbknidti5wpwjbolq
*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*. ...##
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Limited automata and unary languages

2019
*
Information and Computation
*

When d = 1 these models characterize regular

doi:10.1016/j.ic.2019.01.002
fatcat:l4ts3gyqbzfmbh6jjsdz52xb3u
*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] . ...##
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Descriptional and computational complexity of finite automata—A survey

2011
*
Information and Computation
*

Descriptional

doi:10.1016/j.ic.2010.11.013
fatcat:qisoh4k6snfuvbgowrj5bllsli
*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*. ...##
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On the descriptional power of heads, counters, and pebbles

2005
*
Theoretical Computer Science
*

Here we present huge lower bounds for the

doi:10.1016/j.tcs.2004.04.013
fatcat:u2nr4t3twzcubmfoyhfqcn7iwa
*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*. ...##
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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*. ...##
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Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

2001
*
RAIRO - Theoretical Informatics and Applications
*

In particular, we show that, for any m, the number of states necessary

doi:10.1051/ita:2001106
fatcat:zjw2mm2dizdqxpomz64jnj6vlm
*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*. ...##
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Restricted deterministic Watson-Crick automata
[article]

2016
*
arXiv
*
pre-print

We examine the computational power of the restricted model with respect to L being in different

arXiv:1602.05721v1
fatcat:s4szypboqjfvvgjwu75p2orx34
*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*. ...##
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Parikh's Theorem and Descriptional Complexity
[chapter]

2012
*
Lecture Notes in Computer Science
*

) Lower bound: 2 s 2 (from the

doi:10.1007/978-3-642-27660-6_30
fatcat:fjxchgsoljgnjbb3nehc6ydsgq
*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 ...##
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Photonic realization of a quantum finite automaton

2020
*
Physical Review Research
*

We describe a physical implementation of a quantum

doi:10.1103/physrevresearch.2.013089
fatcat:yw7ehwsw45b2dny5olmqqvuwku
*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 * . ...##
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Converting Nondeterministic Automata and Context-Free Grammars into Parikh Equivalent Deterministic Automata
[chapter]

2012
*
Lecture Notes in Computer Science
*

We investigate the conversion of nondeterministic

doi:10.1007/978-3-642-31653-1_26
fatcat:xxrlca7pjjhujglpainm3duwhq
*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*. ...##
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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. ...##
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Unambiguity in Timed Regular Languages: Automata and Logics
[chapter]

2010
*
Lecture Notes in Computer Science
*

A subclass of the two-way deterministic timed

doi:10.1007/978-3-642-15297-9_14
fatcat:dqjhqbzobrbu5iz7zcr3mh6uba
*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. ...
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