Theoretical Informatics and Applications, Aug 17, 2007
Duplication is the replacement of a factor w within a word by ww. This operation can be used iter... more Duplication is the replacement of a factor w within a word by ww. This operation can be used iteratively to generate languages starting from words or sets of words. By undoing duplications, one can eventually reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed. Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication codes exist are fully characterized; the relevant parameters are the duplication length and alphabet size. Finally, some properties of the languages generated by duplication codes are investigated.
Theoretical Informatics and Applications, Jun 15, 2004
We introduce the notion of a differentiation function of a context-free grammar which gives the n... more We introduce the notion of a differentiation function of a context-free grammar which gives the number of terminal words that can be derived in a certain number of steps. A grammar is called narrow (or k-narrow) iff its differentiation function is bounded by a constant (by k). We present the basic properties of differentiation functions, especially we relate them to structure function of contextfree languages and narrow grammars to slender languages. We discuss the decidability of the equivalence of grammars with respect to the differentiation function and structure function and prove the decidability of the k-narrowness of context-free grammars. Furthermore, we introduce languages representing the graph of the differentiation and structure function and relate these languages to those of the Chomsky hierarchy.
Three operations involved in the genome evolution namely, inversion, transposition and duplicatio... more Three operations involved in the genome evolution namely, inversion, transposition and duplication, are considered as operations on strings and languages. We show that, for any pair of these operations, there is a language family which is closed under one of the operations and not closed under the second one, however, under some mild conditions the closure of a language family under one of the operations implies that it also closed with respect to another one.
Hairpin completion is a formal operation inspired from biochemistry. Here we consider a restricte... more Hairpin completion is a formal operation inspired from biochemistry. Here we consider a restricted variant of hairpin completion called bounded hairpin completion. Applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x, hairpin completion produces a new word z, which is a prolongation of x to the right or to the left by annealing. Although this operation is a purely mathematical one and the biological reality is just a source of inspiration, it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion. The restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion. They cannot be longer than a given constant. Closure properties of some classes of formal languages under the non-iterated and iterated bounded hairpin completion are investigated. We consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them. Finally also the inverse operation, namely bounded hairpin reduction, as well as the set of all primitive bounded hairpin roots of a regular language are considered.
We introduce a model that covers the recent studies on Pattern languages (with or without erasing... more We introduce a model that covers the recent studies on Pattern languages (with or without erasing), multi-pattern languages, iterated Pattern languages and languages of Pattern grammars. The model, referred to as a Pattern System, provides a uniform framework for all such studies. Moreover, it gives a new method of investigating certain basic families of developmental languages. This Paper investigates the basics of the main types (general, synchronized, deterministic) of Pattern Systems. Open Problems and topics for further research will be pointed out.
A new dynamical measure of the descriptional complexity for context-free grammars and languages, ... more A new dynamical measure of the descriptional complexity for context-free grammars and languages, namely the degree of cooperation, is introduced and studied. This measure is connected with respect to both families of languages considered, namely the regular and context-free languages. We prove that the degree of cooperation is computable for regular and unambigous context-free grammars and it is not computable for arbitrary context-free grammars. The computability status of this measure for languages remains to be investigated.
The goal of this paper is to survey, in a uniform and systematic way, the main results regarding ... more The goal of this paper is to survey, in a uniform and systematic way, the main results regarding networks of evolutionary processors reported so far. First, we recall the results concerning the computational power of these networks viewed as language generating devices. Then, we briefly present a few NP-complete problems and recall how they were solved in linear time by networks of evolutionary processors with linearly bounded resources (nodes, rules, symbols).
Networks of splicing processors (NSP for short) embody a subcategory among the new computational ... more Networks of splicing processors (NSP for short) embody a subcategory among the new computational models inspired by natural phenomena with theoretical potential to handle unsolvable problems efficiently. Current literature considers three variants in the context of networks managed by random-context filters. Despite the divergences on system complexity and control degree over the filters, the three variants were proved to hold the same computational power through the simulations of two computationally complete systems: Turing machines and 2-tag systems. However, the conversion between the three models by means of a Turing machine is unattainable because of the huge computational costs incurred. This research paper addresses this issue with the proposal of direct and efficient simulations between the aforementioned paradigms. The information about the nodes and edges (i.e., splicing rules, random-context filters, and connections between nodes) composing any network of splicing proces...
Unconventional Computation and Natural Computation, 2019
We continue the investigation of three operations on words and languages with motivations coming ... more We continue the investigation of three operations on words and languages with motivations coming from DNA biochemistry, namely unbounded and bounded hairpin completion and hairpin lengthening. We first show that each of these operations can be used for replacing the third step, the most laborious one, of the solution to the CNF-SAT reported in . As not all the bounded/unbounded hairpin completion or lengthening of semilinear languages remain semilinear, we study sufficient conditions for semilinear languages to preserve their semilinearity property after applying once either the bounded or unbounded hairpin completion, or lengthening. A similar approach is then started for the iterated variants of the three operations. A few open problems are finally discussed.
In this note we consider a new variant of network of splicing processors which simplifies the gen... more In this note we consider a new variant of network of splicing processors which simplifies the general model such that filters remain associated with nodes but the input and output filters of every node coincide. This variant is called {\it network of uniform splicing processors}. Although the communication in the new variant seems less powerful, being based on simpler filters, the new variant is sufficiently powerful to be computationally complete. The main result is that nondeterministic Turing machines can be simulated by networks of uniform splicing processors. Furthermore, the simulation is time efficient.
In this paper, we propose direct simulations between a given network of evolutionary processors w... more In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.
We investigated the computational power of a new variant of network of splicing processors, which... more We investigated the computational power of a new variant of network of splicing processors, which simplifies the general model such that filters remain associated with nodes but the input and output filters of every node coincide. This variant, called network of uniform splicing processors, might be implemented more easily. Although the communication in the new variant seems less powerful, the new variant is sufficiently powerful to be computationally complete. Thus, nondeterministic Turing machines were simulated by networks of uniform splicing processors whose size depends linearly on the alphabet of the Turing machine. Furthermore, the simulation was time efficient. We argue that the network size can be decreased to a constant, namely six nodes. We further show that networks with only two nodes are able to simulate 2-tag systems. After these theoretical results, we discuss a possible software implementation of this model by proposing a conceptual architecture and describe all its...
This work is a survey of the most recent results regarding the computational power of the network... more This work is a survey of the most recent results regarding the computational power of the networks of bio-inspired processors whose communication is based on a new protocol called polarization. In the former models, the communication amongst processors is based on filters defined by some random-context conditions, namely the presence of some symbols and the absence of other symbols. In the new protocol discussed here, a polarization (negative, neutral, and positive) is associated with each node, while the polarization of data navigating through the network is computed in a dynamical way by means of a valuation function. Consequently, the protocol of communication amongst processors is naturally based on the compatibility between their polarization and the polarization of the data. We consider here three types of bio-inspired processors: evolutionary processors, splicing processors, and multiset processors. A quantitative generalization of polarization (evaluation sets) is also presented. We recall results regarding the computational power of these networks considered as accepting devices. Furthermore, a solution to an intractable problem, namely the 0 / 1 Knapsack problem, based on the networks of splicing processors with evaluation sets considered as problem solving devices, is also recalled. Finally, we discuss some open problems and possible directions for further research in this area.
Electronic Proceedings in Theoretical Computer Science, 2009
In this paper, we present some results regarding the size complexity of Accepting Networks of Evo... more In this paper, we present some results regarding the size complexity of Accepting Networks of Evolutionary Processors with Filtered Connections (ANEPFCs). We show that there are universal ANEPFCs of size 10, by devising a method for simulating 2-Tag Systems. This result significantly improves the known upper bound for the size of universal ANEPFCs which is 18. We also propose a new, computationally and descriptionally efficient simulation of nondeterministic Turing machines by ANEPFCs. More precisely, we describe (informally, due to space limitations) how ANEPFCs with 16 nodes can simulate in O(f (n)) time any nondeterministic Turing machine of time complexity f (n). Thus the known upper bound for the number of nodes in a network simulating an arbitrary Turing machine is decreased from 26 to 16.
We consider here two formal operations on words inspired by the DNA biochemistry: hairpin lengthe... more We consider here two formal operations on words inspired by the DNA biochemistry: hairpin lengthening introduced in [15] and its inverse called hairpin shortening. We study the closure of the class of regular languages under the non-iterated and iterated variants of the two operations. The main results are: although any finite number of applications of the hairpin lengthening to a regular language may lead to non-regular languages, the iterated hairpin lengthening of a regular language is always regular. As far as the hairpin shortening operation is concerned, the class of regular languages is closed under bounded and unbounded iterated hairpin shortening. Work supported by the Alexander von Humboldt Foundation Q = Q ∪ Q × Q ∪ Q × Q × {x ∪ [x] ∪ (x)|x ∈ V i , where 0 ≤ i ≤ k}, F = {(q, q, (λ))|q ∈ Q},
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