Florin Manea

Small universal accepting hybrid networks of evolutionary processors

In this paper, we improve some results regarding the size complexity of accepting hybrid networks of evolutionary processors (AHNEPs). We show that there are universal AHNEPs of size 6, by devising a method for simulating 2-tag systems. This result improves the best upper bound for the size of universal AHNEPs which was 7. We also propose a computationally and descriptionally efficient simulation of nondeterministic Turing machines with AHNEPs. More precisely, we prove that AHNEPs with ten nodes can simulate any nondeterministic Turing machine of time complexity f (n) in time O(f (n)). This result significantly improves the best known upper bound for the number of nodes in a network simulating in linear time an arbitrary Turing machine, namely 24.

Networks of evolutionary processors with subregular filters

In this paper we propose a hierarchy of classes of languages, generated by networks of evolutionary processors with the filters in several special classes of regular sets. More precisely, we show that the use of filters from the class of ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite and combinational languages is as powerful as the use of arbitrary regular languages and yields networks that can generate all the recursively enumerable languages. On the other hand, the use of filters that are only finite languages allows only the generation of regular languages, but not all regular languages can be generated. If we use filters that are monoids, nilpotent languages or commutative regular languages, we obtain the same family of languages which contains non-context-free languages but not all regular languages. These results seem to be of interest because they provide both upper and lower bounds on the classes of languages that one can use as filters in a network of evolutionary processor in order to obtain a complete computational model.

Periodicity algorithms for partial words

In this paper we investigate several periodicity-related algorithms for partial words. First, we show that all periods of a partial word of length n are determined in O(n log n) time, and provide algorithms and data structures that help us answer in constant time queries regarding the periodicity of their factors. For this we need a O(n2) preprocessing time and a O(n) updating time, whenever the words are extended by adding a letter. In the second part we show that substituting letters of a word w with holes, with the property that no two holes are too close to each other, to make it periodic can be done in optimal time O(|w|). Moreover, we show that inserting the minimum number of holes such that the word keeps the property can be done as fast.

Networks of evolutionary processors: the power of subregular filters

In this paper, we propose a hierarchy of families of languages generated by networks of evolutionary processors where the filters belong to several special classes of regular sets. More precisely, we show that the use of filters from the class of ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite, and combinational languages is as powerful as the use of arbitrary regular languages and yields networks that can generate all the recursively enumerable languages. On the other hand, the use of filters that are only finite languages allows only the generation of regular languages, but not every regular language can be generated. If we use filters that are monoids, nilpotent languages, or commutative regular languages, we obtain one and the same family of languages which contains non-context-free languages but not all regular languages. These results seem to be of interest because they provide both upper and lower bounds on the families of languages that one can use as filters in a network of evolutionary processors in order to obtain a complete computational model.

On normal forms for networks of evolutionary processors

In this paper we show that some aspects of networks of evolutionary processors can be normalized or simplified without loosing generative power. More precisely, we show that one can use very small finite automata for the control of the communication. We first prove that the networks with evolutionary processors remain computationally complete if one restricts the control automata to have only one state, but underlying graphs of the networks have no fixed structure and the rules are applied in three different modes. Moreover, we show that networks where the rules are applied arbitrary, and all the automata for control have one state, cannot generate all recursively enumerable languages. Finally, we show that one can generate all recursively enumerable languages by complete networks, where the rules are applied arbitrary, but the automata for control have at most two states.

On contextual grammars with subregular selection languages

In this paper, we study the power of external contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families Fn which are obtained by restriction to n states or nonterminals or productions or symbols to accept or to generate regular languages, we obtain four infinite hierarchies of the corresponding families of languages generated by external contextual grammars with selection languages in Fn. Moreover, we give some results on the power of external contextual grammars with regular commutative, regular circular, definite, suffix-free, ordered, combinational, nilpotent, and union-free selection languages.

Complexity-preserving simulations among three variants of accepting networks of evolutionary processors

In this paper we consider three variants of accepting networks of evolutionary processors. It is known that two of them are equivalent to Turing machines. We propose here a direct simulation of one device by the other. Each computational step in one model is simulated in a constant number of computational steps in the other one while a translation via Turing machines squares the time complexity. We also discuss the possibility of constructing simulations that preserve not only complexity, but also the shape of the simulated network.

Deciding according to the shortest computations

In this paper we propose, and analyze from the computational complexity point of view, a new variant of nondeterministic Turing machines. Such a machine accepts a given input word if and only if one of its shortest possible computations on that word is accepting; on the other hand, the machine rejects the input word when all the shortest computations performed by the machine on that word are rejecting. Our main results are two new characterizations of PNP[log] and PNP in terms of the time complexity classes defined for such machines.

Deciding networks of evolutionary processors

In this paper we discuss the usage of Accepting Networks of Evolutionary Processors (ANEPs for short) as deciding devices. In this context we define a new halting condition for this model, which seems more coherent with the rest of the theory than the previous such definition, and show that all the computability results reported so far remain valid in the new framework. Moreover, we give a direct and efficient simulation of an arbitrary ANEP by a complete ANEP, thus, showing that the efficiency of deciding a language by ANEPs is not influenced by the networks topology. Finally, we obtain a surprising characterization of PNP[log] as the class of languages that can be decided in polynomial time by ANEPs.

Unveiling Dynamics and Complexity

Character-based Phylogeny Construction is a well-known combinatorial problem whose input is a matrix M and we want to compute a phylogeny that is compatible with the actual species encoded by M . In this paper we survey some of the known formulations and algorithms for some variants of this problem. Finally, we present the connections between these problems and tumor evolution, and we discuss some of the most important open problems.