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New Results on Alternating and NonDeterministic TwoDimensional FiniteState Automata
 In: Proceedings STACS 2001, LNCS 2010
, 2001
"... . We resolve several longstanding open questions regarding the power of various types of nitestate automata to recognize \picture languages," i.e. sets of twodimensional arrays of symbols. We show that the languages recognized by 4way alternating nitestate automata (AFAs) are incompara ..."
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. We resolve several longstanding open questions regarding the power of various types of nitestate automata to recognize \picture languages," i.e. sets of twodimensional arrays of symbols. We show that the languages recognized by 4way alternating nitestate automata (AFAs) are incomparable to the socalled tiling recognizable languages. Specically, we show that the set of acyclic directed graphs is AFArecognizable but not tiling recognizable, while the set of nonacyclic directed graphs is tiling recognizable but not AFArecognizable. More generally, the complement of an AFArecognizable language is tiling recognizable, and therefore the AFArecognizable languages are not closed under complement. We also show that the set of languages recognized by 4way NFAs is not closed under complement, and that NFAs are more powerful than DFAs, even for languages over one symbol. 1 Introduction Twodimensional words, or \pictures," are rectangular arrays of symbols over a nit...
A characterization of recognizable picture languages by tilings by finite sets
, 2002
"... As extension of the Kleene star to pictures, we introduce the operation of tiling. We give a characterization of recognizable picture languages by intersection of tilings by finite sets of pictures. ..."
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As extension of the Kleene star to pictures, we introduce the operation of tiling. We give a characterization of recognizable picture languages by intersection of tilings by finite sets of pictures.
Algebra of Networks  Modeling simple networks, as well as complex interactive systems
 In: Proof and SystemReliability, Proc. Marktoberdorf Summer School 2001, Kluwer (2002), 4978. A., Sofronia A., Stefanescu G.: Highlevel Structured Interactive
"... The rst part of the paper contains an overview of Network Algebra (NA) book [35]. The second part introduces nite interactive systems as an abstract mathematical model of agents' behaviour and their interaction. ..."
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The rst part of the paper contains an overview of Network Algebra (NA) book [35]. The second part introduces nite interactive systems as an abstract mathematical model of agents' behaviour and their interaction.
Weighted picture automata and weighted logics
 STACS 2006
, 2006
"... We investigate formal power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of twodimensional languages to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a ..."
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We investigate formal power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of twodimensional languages to a quantitative setting. We establish a notion of a weighted MSO logics over pictures. The semantics of a weighted formula will be a picture series. We introduce weighted 2dimensional online tessellation automata (W2OTA) and prove that for commutative semirings, the class of picture series defined by sentences of the weighted logics coincides with the family of picture series that are computable by W2OTA. Moreover, we show that the family of behaviors of W2OTA coincide precisely with the class of picture series characterized by weighted (quadrapolic) picture automata and consequently, the notion of weighted recognizability presented here is robust. However, the weighted structures can not be used to get better decidability properties than in the language case. For every commutative semiring, it is undecidable whether a given MSO formula has restricted structure or whether the semantics of a formula has empty support.
Snakedeterministic tiling systems?
"... Abstract The concept of determinism, while clear and well assessed for string languages, is still matter of research as far as picture languages are concerned. We introduce here a new kind of determinism, called snake, based on the boustrophedonic scanning strategy, that is a natural scanning strat ..."
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Abstract The concept of determinism, while clear and well assessed for string languages, is still matter of research as far as picture languages are concerned. We introduce here a new kind of determinism, called snake, based on the boustrophedonic scanning strategy, that is a natural scanning strategy used by many algorithms on 2D arrays and pictures. We consider a snakedeterministic variant of tiling systems, which defines the socalled SnakeDREC class of languages. SnakeDREC properly extends the more traditional approach of diagonalbased determinism, used e.g. by deterministic tiling systems, and by online tessellation automata. Our main result is showing that the concept of snakedeterminism of tiles coincides with row (or column) unambiguity.
Quantifying SelfOrganization in Cyclic Cellular Automata
 in Noise in Complex Systems and Stochastic Dynamics, Lutz SchimanskyGeier and Derek Abbott and Alexander Neiman and Christian Van den Broeck, Proceedings of SPIE, vol 5114
, 2003
"... Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information theory that let us calculate the dynamical information conte ..."
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Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information theory that let us calculate the dynamical information content of spatial random processes. This complexity measure allows us to quantitatively determine the rate of selforganization of these cellular automata, and establish the relationship between parameter values and selforganization in CCA. The method is very general and can easily be applied to other cellular automata or even digitized experimental data. Keywords: Selforganization, cellular automata, excitable media, cyclic cellular automata, information theory, statistical complexity, spatiotemporal prediction, minimal sufficient statistics
Rectangles and squares recognized by twodimensional automata
 Theory Is Forever, volume 3113 of Lecture Notes in Computer Science
, 2004
"... We consider sets of rectangles and squares recognized by deterministic and nondeterministic twodimensional finitestate automata. We show that NFAs are strictly more powerful than DFAs, even for pictures over a onesymbol alphabet. In the process, we show that the picture languages recognized by N ..."
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We consider sets of rectangles and squares recognized by deterministic and nondeterministic twodimensional finitestate automata. We show that NFAs are strictly more powerful than DFAs, even for pictures over a onesymbol alphabet. In the process, we show that the picture languages recognized by NFAs are not closed under complement, resolving a longstanding open question. We also show that NFAs can only recognize sets of rectangles from the outside that correspond to simple regular languages. Finally, we show that sets of squares recognized by DFAs can be as sparse as any recursively enumerable set. 1.
A CKY parser for picture grammars
"... We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney’s ContextFree Kolam Array grammars (coincident with Matz’s contextfree picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger’ ..."
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We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney’s ContextFree Kolam Array grammars (coincident with Matz’s contextfree picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger’s classical parsing technique for string languages and preserves the polynomial time complexity. Key words: formal languages, picture languages, 2D languages, contextfree picture
Deterministic recognizability of picture languages by Wang automata⋆
"... Picture languages are a generalization of string languages to two dimensions: a picture is a twodimensional array of elements from a finite alphabet. Several classes of picture languages have been considered in the literature [6,8,3,11]. In particular, here we refer to class REC introduced in [6] w ..."
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Picture languages are a generalization of string languages to two dimensions: a picture is a twodimensional array of elements from a finite alphabet. Several classes of picture languages have been considered in the literature [6,8,3,11]. In particular, here we refer to class REC introduced in [6] with the aim to generalize to 2D the class of regular string languages. REC is a robust class that has various characterizations; in particular, it is the class of picture languages that can be generated by tiling systems, a model introduced in [5], or equivalently by Wang systems [4]. A central notion in string regular language theory is determinism, whereas the concept of determinism for picture languages is far from being well understood. Tiling systems are implicitly nondeterministic: REC is not closed under complement, and the membership problem is NPcomplete [9]. Clearly, this latter fact severely hinders the potential applicability of the notation. The identification of a reasonably “rich ” deterministic subset of REC would spur its application, since it would allow linear parsing w.r.t. the number of pixels of the input picture. In past and more recent years, several different deterministic subclasses of REC have been studied, e.g. the classes defined by deterministic 4way automata [8] or deterministic online tessellation acceptors [7]. This latter model inspired the notion of determinism of [1], that relies on four diagonal