Book•
The mathematical theory of L systems
01 Jan 1980-
TL;DR: A survey of the different areas of the theory of developmental systems and languages in such a way that it discusses typical results obtained in each particular problem area.
Abstract: The paper gives a survey of the different areas of the theory of developmental systems and languages. It is organized in such a way that it discusses typical results obtained in each particular problem area. The results quoted may not always be the most important ones but they are quite representative for the direction of research in this theory. Proofs are not given and, consequently, the basic techniques for solving problems in this theory are not discussed. An attempt has been made to cover also the most recent results. Most of the results have not yet appeared in print. To appear in J. Tou (ed. ), Advances in Information Systems Science, Plenum Press.
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TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.
2,327 citations
TL;DR: Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa, and the monadicsecond-order theory of a context-free set of graphs is decidable.
Abstract: The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable.
1,655 citations
TL;DR: The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages and it is suggested that such undecidability is common in these and other dynamical systems.
Abstract: Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata. The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages. Many examples are given. The sizes of the minimal grammars for these languages provide measures of the complexities of the sets. This complexity is usually found to be non-decreasing with time. The limit sets generated by some classes of cellular automata correspond to regular languages. For other classes of cellular automata they appear to correspond to more complicated languages. Many properties of these sets are then formally non-computable. It is suggested that such undecidability is common in these and other dynamical systems.
579 citations
TL;DR: It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet.
Abstract: We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string x over a fixed finite alphabet, selects a context-free grammar G/sub x/ representing x in the sense that x is the unique string belonging to the language generated by G/sub x/. Lossless compression of x takes place indirectly via compression of the production rules of the grammar G/sub x/. It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet. Redundancy bounds for grammar-based codes are established. Reduction rules for designing grammar-based codes are presented.
437 citations
Cites background from "The mathematical theory of L system..."
...First, we need to define the concept of unnormalized entropy, which will be needed in this section and in subsequent parts of the paper....
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TL;DR: A computing model called a tissue P system is proposed, which processes symbols in a multiset rewriting sense, in a net of cells, which can simulate a Turing machine even when using a small number of cells.
Abstract: Starting from the way the inter-cellular communication takes place by means of protein channels (and also from the standard knowledge about neuron functioning), we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (“excitations”) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages is also obtained in this framework. Besides such basic results, the paper provides a series of suggestions for further research.
412 citations
Cites background or methods from "The mathematical theory of L system..."
...3 in [27], we see that any derivation with respect to G starts by several steps of using R1, then R2 is used (exactly once), and the process is iterated; the derivation ends by using R2 (actually, R1 only prepares the string for R2, by changing “the colors” of symbols, never changing the length of the string, while R2 is really changing the strings)....
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...Here we consider only some basic types of L systems and we refer to [27] for details....
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References
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TL;DR: A theory is proposed for the development of filamentous organisms, based on the assumptions that the filaments are composed of cells which undergo changes of state under inputs they receive from their neighbors, and the cells produce outputs as determined by their state and the input they receive.
1,541 citations
TL;DR: The treatment is extended to cases where inputs are received by each cell from both directions along the filament, and the change of state and the output of a cell is determined by its presentState and the two inputs it receives.
844 citations
Book•
01 Jan 1975
TL;DR: Developmental systems were introduced in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms by considering the states and outputs to be identical and thus omitting the output functions.
Abstract: Developmental systems were introduced (Lindenmayer, 1968, 1971) in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms. These systems were originally conceived as linear arrays of interconnected finite automata, each automaton corresponding to a living cell, with the possibility that new automata can be added to the array (cells divide) or be deleted from the array (cells die). Each cell in the array is supposed to have the same state-transition and output functions. As required by biological considerations these functions must be applied to all cells in the array simultaneously at each time step. Thus one obtains infinite sequences of arrays once the functions and the initial arrays are specified. Simplified constructs are defined (and used in this paper) by considering the states and outputs to be identical and thus omitting the output functions. Such filamentous developmental systems have been called “Lindenmayer models” Herman, 1969, 1970) or “L-systems” (Van Dalen, 1971).
423 citations