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Unambiguity in Automata Theory [chapter]

Thomas Colcombet
2015 Lecture Notes in Computer Science  
In this paper, we will investigate the nature of unambiguity in automata theory, presenting the cases of standard finite words up to infinite trees, as well as data-words and tropical automata.  ...  Determinism of devices is a key aspect throughout all of computer science, simply because of considerations of efficiency of the implementation.  ...  Acknowledgment I am really grateful to Jean-Éric Pin, Gabriele Puppis and Michał Skrypczak for their precious help and their discussions on the topic.  ... 
doi:10.1007/978-3-319-19225-3_1 fatcat:wncinjdfmfc6ne4u4pkfy7gjoe

Families of DFAs as Acceptors of omega-Regular Languages

Dana Angluin, Udi Boker, Dana Fisman, Marc Herbstritt
2016 International Symposium on Mathematical Foundations of Computer Science  
Families of dfas (fdfas) provide an alternative formalism for recognizing ω-regular languages.  ...  The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages.  ...  Analyzing the succinctness of saturated fdfas and the complexity of their Boolean operations and decision problems, we believe that they provide an interesting formalism for representing ω-regular languages  ... 
doi:10.4230/lipics.mfcs.2016.11 dblp:conf/mfcs/AngluinBF16 fatcat:ybg5qxphqvci3kpxaip3rfign4

Families of DFAs as Acceptors of ω-Regular Languages [article]

Dana Angluin, Udi Boker, Dana Fisman
2018 arXiv   pre-print
Families of DFAs (FDFAs) provide an alternative formalism for recognizing ω-regular languages.  ...  The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages.  ...  of the recognized language.  ... 
arXiv:1612.08154v2 fatcat:65jk7x5ovzaidmyhtaygegwtie

Nondeterminism in the Presence of a Diverse or Unknown Future [chapter]

Udi Boker, Denis Kuperberg, Orna Kupferman, Michał Skrzypczak
2013 Lecture Notes in Computer Science  
We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata.  ...  Three such classes are nondeterministic automata that are good for trees (GFT; i.e., ones that can be expanded to tree automata accepting the derived tree languages, thus whose choices should satisfy diverse  ...  A Determinization Construction In this section, we show that determinization in the context of GFG automata cannot induce an exponential blowup for both a language and its complement.  ... 
doi:10.1007/978-3-642-39212-2_11 fatcat:dr6tzu5efzd7hkjajjfwqjxpme

Computational complexity in two-level morphology

G. Edward Barton
1986 Proceedings of the 24th annual meeting on Association for Computational Linguistics -  
The use of finite-state machinery in the "twolevel" model by Kimmo Koskenniemi gives it the appearance of computational efficiency, but closer examination shows the model does not guarantee efficient processing  ...  Morphological analysis must take into account the spelling-change processes of a language as well as its possible configurations of stems, affixes, and inflectional markings.  ...  A version of this paper was presented to the Workshop on Finite-State Morphology, Center for the Study of Language and Information, Stanford University, July 29-30, 1985; the author is grateful to Lauri  ... 
doi:10.3115/981131.981140 dblp:conf/acl/Barton86a fatcat:u65udp3amjaknjpawskvc574r4

Descriptional complexity of unambiguous input-driven pushdown automata

Alexander Okhotin, Kai Salomaa
2015 Theoretical Computer Science  
Verbeek, "Input-driven languages are recognized in log n space", FCT 1983), and that this size is necessary in the worst case (R. Alur, P.  ...  This paper demonstrates that the same worst-case 2 Θ(n 2 ) size blow-up occurs when converting a nondeterministic IDPDA to an unambiguous one, and an unambiguous IDPDA to a deterministic one.  ...  [27] gave a more refined construction of witness languages for the NIDPDA determinization blowup, proving that every DIDPDA recognizing those languages must have a certain number of states and a certain  ... 
doi:10.1016/j.tcs.2014.11.015 fatcat:rynx3o46i5dxrjswp3guycc6mu

On the Relative Succinctness of Nondeterministic Büchi and co-Büchi Word Automata [chapter]

Benjamin Aminof, Orna Kupferman, Omer Lev
2008 Lecture Notes in Computer Science  
In this paper we improve the lower bound by showing that for every integer k ≥ 1 there is a language L k over a two-letter alphabet, such that L k can be recognized by an NBW with 2k+1 states, whereas  ...  The practical importance of automata on infinite objects has motivated a re-examination of the complexity of automata-theoretic constructions.  ...  cannot recognize languages that are based on such a tracking.  ... 
doi:10.1007/978-3-540-89439-1_14 fatcat:uz7vjptanbaplk4uxnkykwvxpm

Notes on Counting with Finite Machines

Dmitry Chistikov, Marc Herbstritt
2014 Foundations of Software Technology and Theoretical Computer Science  
We determine the descriptional complexity (smallest number of states, up to constant factors) of recognizing languages {1 n } and {1 tn : t = 0, 1, 2, . . .} with state-based finite machines of various  ...  For visibly pushdown automata, i. e., if the stack movements are determined by input symbols, we consider languages {a n b n } and {a tn b tn : t = 0, 1, 2, . . .} and determine their complexity, of √  ...  Abuzer Yakaryılmaz asked a question on StackExchange that let me come up with a construction of an alternating counter automaton recognizing a non-regular language {1 n : n = 2 k , k = 0, 1, 2, . . .  ... 
doi:10.4230/lipics.fsttcs.2014.339 dblp:conf/fsttcs/Chistikov14 fatcat:5yiv4t4qqvbsrdm7qmcmbujlsa

Describing Periodicity in Two-Way Deterministic Finite Automata Using Transformation Semigroups [chapter]

Michal Kunc, Alexander Okhotin
2011 Lecture Notes in Computer Science  
A framework for the study of periodic behaviour of twoway deterministic finite automata (2DFA) is developed.  ...  A subsemigroup generated by this element represents the behaviour on strings in x + . The main contribution of this paper is a description of all such monogenic subsemigroups up to isomorphism.  ...  Both kinds of automata recognize the same language family as the one-way deterministic finite automata (1DFA).  ... 
doi:10.1007/978-3-642-22321-1_28 fatcat:4xycfjbthncuterrsoigqdfhn4

On the Power of Automata Minimization in Temporal Synthesis [article]

Shufang Zhu, Lucas M. Tabajara, Geguang Pu, Moshe Y. Vardi
2020 arXiv   pre-print
This algorithm first constructs a DFA for the reverse language of the specification and then performs a series of operations to transform it into a minimal DFA for the specification itself.  ...  In theory, the DFA for the reverse language can be exponentially smaller, which would potentially make this algorithm more efficient than directly constructing the DFA for the original specification.  ...  DFA Canonization For every NFA, there exists a unique smallest DFA that recognizes the same language, called the canonical or minimal DFA.  ... 
arXiv:2008.06790v1 fatcat:eub57am5fvhrhnwl5mdwanq7wu

Weight-Reducing Turing Machines [article]

Bruno Guillon, Giovanni Pighizzini, Luca Prigioniero, Daniel Průša
2021 arXiv   pre-print
It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages.  ...  This motivates the introduction of a constructive variant of one-tape machines, called weight-reducing machine, and the investigation of its properties. We focus on the deterministic case.  ...  On the other hand, when the length of the computations, i.e., the time, is linear in the input length, one-tape Turing machines are no more powerful than finite automata, namely they recognize only regular  ... 
arXiv:2103.05486v2 fatcat:hijcczgmcjafhbztq4nk43jd5m

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  
the complement can be described by a language of finite words.  ...  and non-proper equivalence queries (where hypotheses are represented using mod-2-MAs for a related language of finite words). 1 This contrast in learnability results for the class of regular ω-languages  ...  Thus, under the assumption that the systems are finite-state, automata that process infinite words (ω-automata), and the class of languages they recognize -the regular ω-languagesare a useful model for  ... 
doi:10.4230/lipics.csl.2020.8 dblp:conf/csl/AngluinAF20 fatcat:gqrbomby4jcytg57umnctwqdzi

k-Abelian Equivalence and Rationality [chapter]

Julien Cassaigne, Juhani Karhumäki, Svetlana Puzynina, Markus A. Whiteland
2016 Lecture Notes in Computer Science  
Two words u and v are said to be k-abelian equivalent if, for each word x of length at most k, the number of occurrences of x as a factor of u is the same as for v.  ...  We show that the set of lexicographically least representatives of equivalence classes is a regular language. From this we infer that the sequence of the numbers of equivalence classes is N-rational.  ...  The automata in Figure 3 were created using the software Graphviz [4] . We would like to thank the anonymous referees for valuable comments which helped to improve the presentation.  ... 
doi:10.1007/978-3-662-53132-7_7 fatcat:mz66kqgtmnfgvg6mrfg4h4rk2e

On the Power of Automata Minimization in Reactive Synthesis

Shufang Zhu, Lucas M. Tabajara, Geguang Pu, Moshe Y. Vardi
2021 Electronic Proceedings in Theoretical Computer Science  
The most popular language for doing so is Linear Temporal Logic (LTL). Recently, LTL on finite traces, LTL f , has been investigated in several contexts.  ...  In order to reason about LTL f , formulas are typically compiled into deterministic finite automata (DFA), as the intermediate semantic representation.  ...  Acknowledgments Research partially supported by the ERC Advanced Grant WhiteMech (No. 834228), the EU ICT-48 2020 project TAILOR (No. 952215), National Key R&D Program of China (2020AAA0107800), NSF grants  ... 
doi:10.4204/eptcs.346.8 fatcat:65vawwmkczdkda35dzjl43jfnq

Timed pushdown automata revisited [article]

Lorenzo Clemente, Sławomir Lasota
2015 arXiv   pre-print
This paper contains two results on timed extensions of pushdown automata (PDA).  ...  The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass.  ...  'orbit-finite NFA' in sets with equality atoms (N, =) (see [7] for details), and analogously for register pushdown automata [8] .  ... 
arXiv:1503.02422v2 fatcat:bb4ty4pbobfx3auogilc5rlevy
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