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Descriptional Complexity of Bounded Regular Languages [chapter]

Andrea Herrmann, Martin Kutrib, Andreas Malcher, Matthias Wendlandt
2016 Lecture Notes in Computer Science  
Conclusions In this paper, we have studied the descriptional complexity of (strongly) bounded regular languages.  ...  Again, the structure of (strongly) boundedness allows to reduce the descriptional complexity compared with the general case.  ... 
doi:10.1007/978-3-319-41114-9_11 fatcat:if5a2pednfdclmkttvlennedba

Nondeterministic State Complexity of Star-Free Languages [chapter]

Markus Holzer, Martin Kutrib, Katja Meckel
2011 Lecture Notes in Computer Science  
It turns out that in most cases exactly the same tight bounds as for general regular languages are reached.  ...  We investigate the nondeterministic state complexity of several operations on finite automata accepting star-free languages.  ...  More than a decade ago the operation problem for regular languages represented by deterministic finite automata (DFAs) as studied in [32, 33] renewed the interest in descriptional complexity issues of  ... 
doi:10.1007/978-3-642-22256-6_17 fatcat:hykuruuj3nh53eyx7gxbsmtfc4

Nondeterministic Biautomata and Their Descriptional Complexity [chapter]

Markus Holzer, Sebastian Jakobi
2013 Lecture Notes in Computer Science  
Descriptional complexity issues for deterministic biautomata were addressed in [3] .  ...  We focus on the descriptional complexity of nondeterministic biautomata, which are defined as follows: a nondeterministic biautomaton is a sixtuple A = (Q, Σ, ·, •, I, F ), where Q is a finite set of states  ... 
doi:10.1007/978-3-642-39310-5_12 fatcat:d5hubjip2jdoxmrrbr3yvqufbm


2014 International Journal of Foundations of Computer Science  
Descriptional complexity issues for deterministic biautomata were addressed in [3] .  ...  We focus on the descriptional complexity of nondeterministic biautomata, which are defined as follows: a nondeterministic biautomaton is a sixtuple A = (Q, Σ, ·, •, I, F ), where Q is a finite set of states  ... 
doi:10.1142/s0129054114400115 fatcat:mpyyfyxwtvdmvjogim2ojbpuum

On Measuring Non-Recursive Trade-Offs

Hermann Gruber, Markus Holzer, Martin Kutrib
2009 Electronic Proceedings in Theoretical Computer Science  
We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences  ...  We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion.  ...  We first establish some notation for descriptional complexity. In order to be general, we formalize the intuitive notion of a representation or description of a family of languages.  ... 
doi:10.4204/eptcs.3.13 fatcat:iwyn6aly6zbslj2qxx6kzf2u4m

Descriptional Complexity of Deterministic Regular Expressions [chapter]

Katja Losemann, Wim Martens, Matthias Niewerth
2012 Lecture Notes in Computer Science  
We study the descriptional complexity of regular languages that are definable by deterministic regular expressions.  ...  Then we give an overview of the closure properties of these languages under various language-theoretic operations and we study the descriptional complexity of applying these operations.  ...  Descriptional Complexity of Operations on DRE-Definable Languages We are now ready to apply previously obtained results to prove lower bounds on the descriptional complexity of operations on DREs.  ... 
doi:10.1007/978-3-642-32589-2_56 fatcat:kdz6adftwjg4vbgnzs7v7tpv24

A Survey on Operational State Complexity [article]

Yuan Gao and Nelma Moreira and Rogério Reis and Sheng Yu
2015 arXiv   pre-print
Descriptional complexity is the study of the conciseness of the various models representing formal languages.  ...  In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages.  ...  State complexity is a type of descriptional complexity based on the finite machine model, and, in the domain of regular languages, it is related to the basic question of how to measure the size of a finite  ... 
arXiv:1509.03254v1 fatcat:oxleg7kkvvezxoqgscdnlghzvu

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

Martin Kutrib, Andreas Malcher, Matthias Wendlandt
2013 Lecture Notes in Computer Science  
The descriptional complexity of unary regular languages has been studied in many ways.  ...  Introduction One of the main topics of descriptional complexity is the question of how the size of the description of a formal language varies when being described by different formalisms.  ... 
doi:10.1007/978-3-642-39310-5_15 fatcat:odbv4r7jtbbknidti5wpwjbolq

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.  ... 

On the descriptional power of heads, counters, and pebbles

Martin Kutrib
2005 Theoretical Computer Science  
We investigate the descriptional complexity of deterministic two-way k-head finite automata (k-DHA).  ...  It is shown that between non-deterministic pushdown automata and any k-DHA, k 2, there are savings in the size of description which cannot be bounded by any recursive function.  ...  In particular, it is studied whether there exist upper bounds for the increase in complexity when changing from a minimal description of a language by non-deterministic pushdown automata to an equivalent  ... 
doi:10.1016/j.tcs.2004.04.013 fatcat:u2nr4t3twzcubmfoyhfqcn7iwa

Transition Complexity of Incomplete DFAs

Yuan Gao, Kai Salomaa, Sheng Yu
2010 Electronic Proceedings in Theoretical Computer Science  
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained.  ...  However, for intersection, the transition complexity result is similar to that of state complexity.  ...  Acknowledgement We would like to thank the anonymous referees of DCFS2010 for their careful reading and valuable suggestions.  ... 
doi:10.4204/eptcs.31.12 fatcat:eapxqlwnpfbwfinbibtaaqbhaq

Succinctness of descriptions of SBTA-languages

Jozef Gruska, Angelo Monti, Margherita Napoli, Domenico Parente
1997 Theoretical Computer Science  
Moreover, we compare the state-complexity of regular languages with respect to their description by deterministic finite automata and several types of SBTA.  ...  First we provide various criteria to determine lower bounds on the state-complexity of an SBTA-language L, that is bounds on the minimum number of states for an SBTA to accept L, and we show the existence  ...  By complexity of description of a language it is generally understood the minimal size of the description of some device describing the language.  ... 
doi:10.1016/s0304-3975(96)00133-8 fatcat:gbtdjc3owfgezkjui4u2j5d4pq

State Complexity of Suffix Distance [chapter]

Timothy Ng, David Rappaport, Kai Salomaa
2017 Lecture Notes in Computer Science  
The neighbourhood of a regular language with respect to the prefix, suffix and subword distance is always regular and a tight bound for the state complexity of prefix distance neighbourhoods is known.  ...  We give upper bounds for the state complexity of the neighbourhood of radius k of an n state DFA (deterministic finite automaton) language with respect to the suffix distance and the subword distance,  ...  We do not have a lower bound construction matching the upper bound of Proposition 4 for the state complexity of subword distance neighbourhoods.  ... 
doi:10.1007/978-3-319-60252-3_23 fatcat:dsv4obgprfbrzos2r6e5rxnlqq

Incomplete Transition Complexity of Basic Operations on Finite Languages [chapter]

Eva Maia, Nelma Moreira, Rogério Reis
2013 Lecture Notes in Computer Science  
For all operations we give tight upper bounds for both descriptional measures.  ...  The state complexity of basic operations on finite languages (considering complete DFAs) has been extensively studied in the literature.  ...  Introduction Descriptional complexity studies the measures of complexity of languages and operations.  ... 
doi:10.1007/978-3-642-39274-0_31 fatcat:2tzas46rdfcvzjpaktgxsdgs2q

Transition complexity of language operations

Michael Domaratzki, Kai Salomaa
2007 Theoretical Computer Science  
This work extends previous work on descriptional complexity of regular language operations, in particular, under the measures of deterministic state complexity, nondeterministic state complexity and regular  ...  There has been a significant amount of work related to the trade-off between the number of transitions and other descriptional complexity measures for regular languages.  ...  We thank Lane Hemaspaandra for pointing out an error in a previous version of Theorem 6.  ... 
doi:10.1016/j.tcs.2007.07.034 fatcat:yl46z3egsbgqxg4oe2udgomuwq
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