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Linear Grammars with One-Sided Contexts and Their Automaton Representation [chapter]

Mikhail Barash, Alexander Okhotin
2014 Lecture Notes in Computer Science  
The same construction proves the Σ 0 2 -completeness of the finiteness problem for these grammars and automata.  ...  These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel.  ...  Automaton representation Linear conjunctive grammars are known to be computationally equivalent to one of the simplest types of cellular automata: the one-way real-time cellular automata, also known under  ... 
doi:10.1007/978-3-642-54423-1_17 fatcat:e63ob2llvrdh5dx5uf7yhenpyu

A simple P-complete problem and its language-theoretic representations

Alexander Okhotin
2011 Theoretical Computer Science  
This is the family of linear conjunctive grammars, which is notable for being computationally equivalent to trellis automata [19] , also known as one-way real-time cellular automata [2] [3] [4] 10, 27]  ...  A natural P -complete problem for time-bounded cellular automata was recently found by Neary and Woods [15] . Results of this kind are equally important for formal grammars.  ...  of cellular automata, which will now be defined.  ... 
doi:10.1016/j.tcs.2010.09.015 fatcat:sbpjiaqdwrf2bkkvaac7o44ivu

Input-driven languages are linear conjunctive

Alexander Okhotin
2016 Theoretical Computer Science  
Linear conjunctive grammars define the same family of languages as one-way real-time cellular automata (A.  ...  Okhotin, "On the equivalence of linear conjunctive grammars to trellis automata", RAIRO ITA, 2004), and this family is known to be incomparable with the context-free languages (V.  ...  Linear conjunctive grammars are notable for having an equivalent representation by one of the simplest types of cellular automata.  ... 
doi:10.1016/j.tcs.2016.01.007 fatcat:4siifi2asvchhcc4ftxrwtew34

Linear grammars with one-sided contexts and their automaton representation

Mikhail Barash, Alexander Okhotin
2015 RAIRO - Theoretical Informatics and Applications  
The same construction proves the Σ 0 2 -completeness of the finiteness problem for these grammars and automata.  ...  These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel.  ...  Automaton representation Linear conjunctive grammars are known to be computationally equivalent to one of the simplest types of cellular automata: the one-way real-time cellular automata, also known under  ... 
doi:10.1051/ita/2015004 fatcat:nhymxnzwq5bvzmx5jemgl2zwp4

Descriptive complexity for minimal time of cellular automata [article]

Étienne Grandjean, Théo Grente
2019 arXiv   pre-print
Our paper establishes logical characterizations of the three classical complexity classes that model minimal time, called real-time, of one-dimensional cellular automata according to their canonical variants  ...  This is important for parallel computation models such as cellular automata, because designing parallel programs is considered difficult.  ...  Her teaching, her deep insights into cellular automata, the references and advice she generously gave us, as well as her careful reading, were essential in designing and finalizing our concepts and results  ... 
arXiv:1902.05720v2 fatcat:qmb3fnscdbhtzkhhls3s4xbsnq

Representing a P-complete problem by small trellis automata

Alexander Okhotin
2009 Electronic Proceedings in Theoretical Computer Science  
A restricted case of the Circuit Value Problem known as the Sequential NOR Circuit Value Problem was recently used to obtain very succinct examples of conjunctive grammars, Boolean grammars and language  ...  In this paper, a new encoding of the same problem is proposed, and a trellis automaton (one-way real-time cellular automaton) with 11 states solving this problem is constructed.  ...  Trellis automata and conjunctive grammars Trellis automata can be equally defined by their cellular automata semantics (using evolution of configurations) and through the trellis representing their computation  ... 
doi:10.4204/eptcs.1.18 fatcat:vac2b5c3hrdprjvcp5mv7ipnly

Page 8113 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
Amano and Kazuo Iwama, An unsolvable problem concerning quantum finite automata (200- 205); Takahiro Hori, Katsunobu Imai and Kenichi Morita, 3- dimensional reversible self-reproducing cellular automata  ...  be- havior of conjunctive learning algorithms (123-129).  ... 

Conjunctive and Boolean grammars: The true general case of the context-free grammars

Alexander Okhotin
2013 Computer Science Review  
This paper surveys the results on conjunctive and Boolean grammars obtained over the last decade, comparing them to the corresponding results for ordinary context-free grammars and their main subfamilies  ...  Conjunctive grammars extend the definition of a context-free grammar by allowing a conjunction operation in the rules; Boolean grammars are further equipped with an explicit negation.  ...  This is the family defined by one of the simplest types of cellular automata: the one-way real-time cellular automata, also known under the proper name of trellis automata, studied by Dyer [21] ,Čulík  ... 
doi:10.1016/j.cosrev.2013.06.001 fatcat:vjrnokycqres5mfpdupksfaumm

Page 1209 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
Truan, On cellular graph-automata and second-order definable graph-properties (pp. 384-393); Jifi Vinarek, Extensions of symmetric hom-functors to the Kleisli category (pp. 394-399); J.  ...  Sain, First order dynamic logic with decidable proofs and workable model theory (pp. 334-340); Detlef Seese, Elimination of second-order quantifiers for well-founded trees in stationary logic and finitely  ... 

Boolean grammars

Alexander Okhotin
2004 Information and Computation  
cubic-time recognition algorithm and some limited extension of the notion of a parse tree, which together allow to conjecture practical applicability of the new concept.  ...  A new generalization of context-free grammars is introduced: Boolean grammars allow the use of all settheoretic operations as an integral part of the formalism of rules.  ...  It has been proposed that the relationship between trellis automata and linear conjunctive grammars resembles that between finite automata and regular expressions [26] .  ... 
doi:10.1016/j.ic.2004.03.006 fatcat:72ahhppp7rdu7dh522atfhgq7u

Boolean Grammars [chapter]

Alexander Okhotin
2003 Lecture Notes in Computer Science  
cubic-time recognition algorithm and some limited extension of the notion of a parse tree, which together allow to conjecture practical applicability of the new concept.  ...  A new generalization of context-free grammars is introduced: Boolean grammars allow the use of all settheoretic operations as an integral part of the formalism of rules.  ...  It has been proposed that the relationship between trellis automata and linear conjunctive grammars resembles that between finite automata and regular expressions [26] .  ... 
doi:10.1007/3-540-45007-6_32 fatcat:3dlwyybfmnbwbmvn6v6llfxfhm

Subject index volumes 1–200

1999 Theoretical Computer Science  
, 3832 finite state asynchronous cellular automata. 2505 finite state automata, 227, 472 guaranteeing viability, 2625 state minimization of -, 786 with multiplicities, 227 finite state cellular automata  ...  , 640 unguarded agents, 1415 Ungureanu, foundations of mathematics, logic and computer concurrency control and recovery, 363 I effectivity, 738 grammars and machines, 725 interconnection network structure  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Models for quantitative distributed systems and multi-valued logics

Martin Huschenbett
2013 International Journal of Computer Mathematics  
We prove that weighted asynchronous cellular automata and weighted finite automata which satisfy an I-diamond property are equally expressive.  ...  We investigate weighted asynchronous cellular automata with weights in valuation monoids. These automata form a distributed extension of weighted finite automata and allow us to model concurrency.  ...  The syntax of weighted MSO logic over Σ and D (wMSO logic for short) is given by the grammar Product valuation monoids and weighted MSO logic for Σ-posets β ::= x ≤ y | λ(x) = a | x ∈ X | ¬β | β ∧ β  ... 
doi:10.1080/00207160.2012.702211 fatcat:xzrxiclfcngtpiu6g5u7ltf43q

Models for Quantitative Distributed Systems and Multi-Valued Logics [chapter]

Martin Huschenbett
2011 Lecture Notes in Computer Science  
We prove that weighted asynchronous cellular automata and weighted finite automata which satisfy an I-diamond property are equally expressive.  ...  We investigate weighted asynchronous cellular automata with weights in valuation monoids. These automata form a distributed extension of weighted finite automata and allow us to model concurrency.  ...  The syntax of weighted MSO logic over Σ and D (wMSO logic for short) is given by the grammar Product valuation monoids and weighted MSO logic for Σ-posets β ::= x ≤ y | λ(x) = a | x ∈ X | ¬β | β ∧ β  ... 
doi:10.1007/978-3-642-21254-3_24 fatcat:3byda34s3zbyfayvegpoj6s6ee

Abstracts of Current Computer Literature

1970 IEEE transactions on computers  
Arbitrary Logic Gates as Logic Modules for Realizing Boolean Functions 7355 189 IEEE TRANSACTIONS ON COMPUTERS, FEBRUARY 1970 Microprogramming and Stored Logic 7371 Integrated Circuit Cellular  ...  In this paper the specific engineering features of such cellular logic-in-memory (CLIM) arrays are discussed, and one such special-purpose array, a cellular sorting array, is described in detail to illustrate  ... 
doi:10.1109/t-c.1970.222892 fatcat:tpn743oi6za4dfhaudkprjabmm
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