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Thermodynamics and Complexity of Cellular Automata

Remo Badii, Antonio Politi
1997 Physical Review Letters  
formalism is applied to the limit spatial configuration.  ...  In particular, it is shown that the elementary rule 22 is able to produce, upon iteration, a deep nesting of grammatical rules and that this asymptotically yields a phase transition when the thermodynamic  ...  The agreement between the two approaches strengthens the validity of the numerical findings [16] .  ... 
doi:10.1103/physrevlett.78.444 fatcat:qciqetdcqrbntlndbnugf7t7j4

The Degree of Irreversibility in Deterministic Finite Automata

Holger Bock Axelsen, Markus Holzer, Martin Kutrib
2017 International Journal of Foundations of Computer Science  
The recent DFA method essentially works by minimizing the DFA and inspecting it for a forbidden pattern.  ...  We here study the degree of irreversibility for a regular language, the minimal number of such forbidden patterns necessary in any DFA accepting the language, and show that the degree induces a strict  ...  This suggests that the forbidden pattern captures an essential aspect of irreversibility, and offers an approach to studying the gap between the reversibly regular and regular languages based on the absence  ... 
doi:10.1142/s0129054117400044 fatcat:h7xwtikzf5fv5nnyvk4rmbs35y

The Boolean Hierarchy over Level 1/2 of the Straubing-Therien Hierarchy [article]

Heinz Schmitz, Klaus W. Wagner
1998 arXiv   pre-print
Moreover we prove a "forbidden-pattern" characterization of L(1) of the type: L is in L(1) if and only if a certain pattern does not appear in the transition graph of a deterministic finite automaton accepting  ...  From this criterion we can conclude that this boolean hierarchy is proper and that its classes are decidable.In finite model theory the latter implies the decidability of the classes of the boolean hierarchy  ...  There is a close connection between concatenation hierarchies and complexity classes, both related via the so-called leaf language approach to define complexity classes.  ... 
arXiv:cs/9809118v1 fatcat:gez5cgx7efgjhevgwqthywniq4

Languages polylog-time reducible to dot-depth 1/2

Christian Glaßer
2007 Journal of computer and system sciences (Print)  
For both classes we provide • forbidden-pattern characterizations, and • characterizations in terms of regular expressions. This implies that both classes are decidable.  ...  We construct star-free regular languages L n such that L n 's balanced leaf-language class is NP, but the unbalanced leaf-language class of L n contains level n of the unambiguous alternation hierarchy  ...  Acknowledgments The author thanks Bernhard Schwarz, Victor Selivanov, and Klaus W. Wagner for exciting discussions about leaf languages and reducibility notions for star-free languages.  ... 
doi:10.1016/j.jcss.2006.09.004 fatcat:2pwxmb63yrbcrh75ixflfjm7ea

Algebraic Theory of Patterns as Generalized Symmetries

Adam Rupe, James P. Crutchfield
2022 Symmetry  
As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns.  ...  We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence.  ...  The authors also thank the Telluride Science Research Center for hospitality during visits and the participants of the Information Engines Workshops there. JPC acknowledges the kind  ... 
doi:10.3390/sym14081636 fatcat:ofmuenddg5gubi37xhni73pyya

Algebraic Theory of Patterns as Generalized Symmetries [article]

Adam Rupe, James P. Crutchfield
2022 arXiv   pre-print
As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns.  ...  We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence.  ...  The authors also thank the Telluride Science Research Center for hospitality during visits and the participants of the Information Engines Workshops there. AR acknowledges the support of the U.S.  ... 
arXiv:2206.15050v1 fatcat:d4a5fyrpunbdjd3ufokroya4qq

Efficient algorithms for membership in boolean hierarchies of regular languages

Christian Glaßer, Heinz Schmitz, Victor Selivanov
2016 Theoretical Computer Science  
We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: • The classes of the Boolean hierarchy over level Σ1 of the dot-depth hierarchy  ...  The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known.  ...  Acknowledgements We are grateful to Klaus W. Wagner for many helpful discussions. We would like to thank the anonymous referees for their valuable comments.  ... 
doi:10.1016/j.tcs.2016.07.017 fatcat:tqu5qwscmbbbvebstf2lkexy2m

Cairne Arabic Syllable Structure though Different Phonological Theories

Rajaa Aquil
2013 Open Journal of Modern Linguistics  
It is through the generative Optimality Theoretic approach that more than one phenomenon can be described and analyzed.  ...  heavy word internally, limitations on consonant clusters in certain positions of a word, and epenthesis of a vowel to break consonant clusters if there happen to be more than two consonants in word concatenation  ...  All these approaches added to the theory of the syllable. The aim of the present paper is not to compare between the different phonological theories.  ... 
doi:10.4236/ojml.2013.33034 fatcat:3eoyzyyfo5da5av6bj66lftzoi

Weakly and Strongly Irreversible Regular Languages

Giovanna J. Lavado, Giovanni Pighizzini, Luca Prigioniero
2017 Electronic Proceedings in Theoretical Computer Science  
This gives an infinite hierarchy of weakly irreversible languages, i.e., languages which are k-reversible for some k.  ...  Furthermore, a construction which allows to transform any finite automaton which is not k-reversible, but which accepts a k-reversible language, into an equivalent k-reversible finite automaton, is presented  ...  Acknowledgment We thank the anonymous referees for valuable suggestions, in particular for addressing us to consider the results obtained in [8] .  ... 
doi:10.4204/eptcs.252.15 fatcat:fmpv5rfiufdlnpa4xvud4rsc6u

Machines that Can Output Empty Words

Christian Glaßer, Stephen Travers
2007 Theory of Computing Systems  
Inspired by the neutral behavior of rejecting paths of NP machines, we allow transducers to output empty words. The paper explains several advantages of the new model.  ...  A central aspect is that it allows us to prove strong gap theorems: For any class C that is definable in the e-model, either coUP ⊆ C or C ⊆ NP.  ...  This is possible by the e-model's tight connection to the STH, by the forbidden-pattern characterization of Σ FO 2 which was proved by Pin and Weil [PW97] , and by the equality Leaf p u (Σ FO 2 ) = ∆  ... 
doi:10.1007/s00224-007-9087-5 fatcat:ztduhoeczjbo5e4eqkloyfoga4

Machines that Can Output Empty Words [chapter]

Christian Glaßer, Stephen Travers
2006 Lecture Notes in Computer Science  
Inspired by the neutral behavior of rejecting paths of NP machines, we allow transducers to output empty words. The paper explains several advantages of the new model.  ...  A central aspect is that it allows us to prove strong gap theorems: For any class C that is definable in the e-model, either coUP ⊆ C or C ⊆ NP.  ...  This is possible by the e-model's tight connection to the STH, by the forbidden-pattern characterization of Σ FO 2 which was proved by Pin and Weil [PW97] , and by the equality Leaf p u (Σ FO 2 ) = ∆  ... 
doi:10.1007/11821069_38 fatcat:aziyx7bfpzgo3if4oor673jrji

Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages [article]

Christian Glasser, Heinz Schmitz, Victor Selivanov
2008 arXiv   pre-print
We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: - The classes of the Boolean hierarchy over level Σ_1 of the dot-depth hierarchy  ...  The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known.  ...  Acknowledgements We are grateful to Klaus W. Wagner for many helpful discussions. We would like to thank the anonymous referees for their valuable comments.  ... 
arXiv:0802.2868v1 fatcat:euqbn7hprrgdbkqnuocyqwhxyu

Using Model Theory for Grammatical Inference: a Case Study from Phonology

Kristina Strother-Garcia, Jeffrey Heinz, Hyun Jin Hwangbo
2016 International Conference on Grammatical Inference  
Model-theoretic approaches to formal language theory have traditionally assumed that each position in a string belongs to exactly one unary relation.  ...  This paper examines the characterization and learning of grammars defined by conjunctions of negative and positive literals (CNPL) where the literals correspond to structures in an enriched model theory  ...  Rather than move up the hierarchy, Heinz suggests L is innate and does not need to be learned.  ... 
dblp:conf/icgi/Strother-Garcia16 fatcat:b52b66ql25a3dapyvkhk5ukzea

The Dot-Depth Hierarchy, 45 Years Later [chapter]

Jean-Éric Pin
2017 The Role of Theory in Computer Science  
This survey article reports on the numerous results and conjectures attached to this hierarchy.  ...  This hierarchy and its generalisations, together with the problems attached to them, had a long-lasting influence on the development of automata theory.  ...  Acknowledgments I would like to thank Jeffrey Shallit for his kind invitation to the Brzozowski's conference and for his useful comments on this paper.  ... 
doi:10.1142/9789813148208_0008 dblp:conf/birthday/Pin17a fatcat:u54iyat4cbgl7ov2eu64xhktma

Subregular Complexity and Deep Learning [article]

Enes Avcu, Chihiro Shibata, Jeffrey Heinz
2017 arXiv   pre-print
Second, the s-RNNs out-performed the LSTMs on the most complex SP experiment and performed comparably to them on the others.  ...  The SL and SP classes are among the simplest in a mathematically well-understood hierarchy of subregular classes. They encode local and long-term dependencies, respectively.  ...  We are grateful to the feedback of the audiences of the LAML conference, the LearnAut workshop and the IACS seminar.  ... 
arXiv:1705.05940v3 fatcat:2xftnyzxkvdwpfud4kifomn6ve
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