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On binary ⊕-NFAs and succinct descriptions of regular languages

Lynette van Zijl
2004 Theoretical Computer Science  
We prove a new lower bound for the number of distinct languages accepted by binary symmetric difference automata (⊕-NFAs), and compare that to Domaratzki's results (J.  ...  We also show that there are certain regular languages which are accepted by succinct ⊕-NFAs, but for which no succinct traditional NFA exists.  ...  Finally, in Section 4, we look at the relationship between the set of regular languages which have succinct descriptions with ⊕-NFAs, and the set of regular languages which have succinct descriptions with  ... 
doi:10.1016/j.tcs.2004.07.012 fatcat:3ldymdz7wjhd3be7sts5rtgprm

Succinct Descriptions of Regular Languages with Binary ⊕-NFAs [chapter]

Lynette van Zijl
2003 Lecture Notes in Computer Science  
We then consider the number of distinct languages accepted by binary ⊕-NFAs, and compare that to Domaratzki's results [2] for (traditional) binary NFAs.  ...  We also show that there are certain regular languages which are accepted by succinct ⊕-NFAs, but for which no succinct traditional NFA exists.  ...  We next consider the relationship between regular languages having a succinct description using traditional NFAs on the one hand, and ⊕-NFAs on the other hand.  ... 
doi:10.1007/3-540-45089-0_8 fatcat:l4njiinq4rap3obvoubnrhbzfu

Ambiguity, Nondeterminism and State Complexity of Finite Automata

Yo-Sub Han, Arto Salomaa, Kai Salomaa
2017 Acta Cybernetica  
This paper surveys work on the degree of ambiguity and on various nondeterminism measures for finite automata.  ...  The degree of ambiguity counts the number of accepting computations of a nondeterministic finite automaton (NFA) on a given input.  ...  Acknowledgements Han was supported by the Basic Science Research Program through NRF funded by MEST (2015R1D1A1A01060097) and the Yonsei University Future-leading Re-  ... 
doi:10.14232/actacyb.23.1.2017.9 fatcat:zoahl3ij65bhbpms5d24xkc4i4

Structurally Unambiguous Finite Automata [chapter]

Hing Leung
2006 Lecture Notes in Computer Science  
We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q0 such that for all input strings w and for any state q, there is at  ...  We show that SUFA can be exponentially more succinct in the number of states than UFA and MDFA (deterministic finite automata with multiple initial states).  ...  In Section 2, we have shown that SUFA can be exponentially more succinct than UFA and MDFA (also, reversals of MDFA) for denoting some family of regular languages.  ... 
doi:10.1007/11812128_19 fatcat:6wz6i2vqpvc3zajjp4nlzt2ue4

Page 9261 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
, Rémi (D-TUD-AL; Dresden) On regular message sequence chart languages and relationships to Mazurkiewicz trace theory.  ...  This enables us to prove our main result: one can decide whether the iteration of a given regular language of MSCs is regular if, and only if, the star problem in trace monoids (over some restricted independence  ... 

Complexity of Counting First-Order Logic for the Subword Order

Dietrich Kuske, Christian Schwarz, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
The main result shows that the two-variable fragment of this logic can be decided in two-fold exponential space provided the regular predicates are restricted to piecewise testable ones.  ...  This paper considers the structure consisting of the set of all words over a given alphabet together with the subword relation, regular predicates, and constants for every word.  ...  There are different characterisations of piecewise testable languages using nfas, we only rely on one by Masopust and Thomazo [15, 16] : a pt-nfa is a partially ordered and complete nfa that satisfies  ... 
doi:10.4230/lipics.mfcs.2020.61 dblp:conf/mfcs/KuskeS20 fatcat:ydanpbabhfgyzayqcvbdd5scpa

A Survey on Operational State Complexity [article]

Yuan Gao and Nelma Moreira and Rogério Reis and Sheng Yu
2015 arXiv   pre-print
In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages.  ...  Descriptional complexity is the study of the conciseness of the various models representing formal languages.  ...  On the other hand, for a given regular language there may be more than one minimal NFA and NFA minimization is PSPACE-hard [94, 178] .  ... 
arXiv:1509.03254v1 fatcat:oxleg7kkvvezxoqgscdnlghzvu

On the Complexity of Determinizing Monitors [chapter]

Luca Aceto, Antonis Achilleos, Adrian Francalanza, Anna Ingólfsdóttir, Sævar Örn Kjartansson
2017 Lecture Notes in Computer Science  
We examine the determinization of monitors. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor.  ...  When (deterministic) monitors are described as finite automata (as their LTS), then they can be exponentially more succinct than their CCS process form. ?  ...  As a matter of fact, non-deterministic monitor descriptions are often more succinct than deterministic ones, and thus easier to formulate and comprehend.  ... 
doi:10.1007/978-3-319-60134-2_1 fatcat:2ijejls62ncxnct4ym27gzfegm

Strongly Unambiguous Büchi Automata Are Polynomially Predictable With Membership Queries

Dana Angluin, Timos Antonopoulos, Dana Fisman, Michael Wagner
2020 Annual Conference for Computer Science Logic  
a regular language using membership queries and equivalence queries.  ...  However, many interesting properties of reactive systems, in particular, liveness and fairness, require richer classes of regular ω-languages.  ...  Given that DFAs, UFAs, NFAs and mod-2-MAs all accept the class of regular languages, an important distinction between them is succinctness, the number of states in the smallest automaton to accept a given  ... 
doi:10.4230/lipics.csl.2020.8 dblp:conf/csl/AngluinAF20 fatcat:gqrbomby4jcytg57umnctwqdzi

From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

Hermann Gruber, Markus Holzer
2014 Electronic Proceedings in Theoretical Computer Science  
Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination  ...  In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa.  ...  Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper.  ... 
doi:10.4204/eptcs.151.2 fatcat:xiiyglxcebbkpdklmkngqd47dm

From Finite Automata to Regular Expressions and Back — A Summary on Descriptional Complexity

Hermann Gruber, Markus Holzer
2015 International Journal of Foundations of Computer Science  
Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination  ...  In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa.  ...  Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper.  ... 
doi:10.1142/s0129054115400110 fatcat:glifsfoc4jgw7cpuyxjwlwcq6a

Descriptional and computational complexity of finite automata—A survey

Markus Holzer, Martin Kutrib
2011 Information and Computation  
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].  ...  Descriptional and Computational Complexity of Finite Automata, Proc. 3rd Int. Conf. Language M. Holzer, M.  ...  For a survey on the descriptional complexity of the operation problem for DFAs and NFAs we refer to [87] and [37, 38] . Let • be a fixed operation on languages that preserves regularity.  ... 
doi:10.1016/j.ic.2010.11.013 fatcat:qisoh4k6snfuvbgowrj5bllsli

The Magic Number Problem for Subregular Language Families

Markus Holzer, Sebastian Jakobi, Martin Kutrib
2010 Electronic Proceedings in Theoretical Computer Science  
It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified.  ...  We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free  ...  For recent surveys on descriptional complexity issues of regular languages we refer to, for example, [6, 7, 8] .  ... 
doi:10.4204/eptcs.31.13 fatcat:ytpmydmnq5bmrp5nv4n6qqwjra

More on Deterministic and Nondeterministic Finite Cover Automata [chapter]

Hermann Gruber, Markus Holzer, Sebastian Jakobi
2015 Lecture Notes in Computer Science  
Finite languages are an important sub-regular language family, which were intensively studied during the last two decades in particular from a descriptional complexity perspective.  ...  Finally, we present some results on the average size of finite cover automata.  ...  In particular, for regular languages and subfamilies one may use deterministic (DFAs) or nondeterministic finite automata (NFAs) or variants thereof to describe these languages.  ... 
doi:10.1007/978-3-319-22360-5_10 fatcat:xezi36ob3bcirfm3ssikhhtyuq

Minimizing NFA's and Regular Expressions [chapter]

Gregor Gramlich, Georg Schnitger
2005 Lecture Notes in Computer Science  
Our inapproximability results for a given dfa with n states are based on cryptographic assumptions and we show that any efficient algorithm will have an approximation factor of at least n poly(log n) .  ...  We show inapproximability results concerning minimization of nondeterministic finite automata (nfa's) as well as regular expressions relative to given nfa's, regular expressions or deterministic finite  ...  Solution: The size of a smallest nfa equivalent with D. Measure: Number of states or transitions. Bad News: Optimal solution cannot be determined efficiently.  ... 
doi:10.1007/978-3-540-31856-9_33 fatcat:62akhfsipfc4vnp4t7skenc64e
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