Peter Leupold

Evolution and observation: a non-standard way to generate formal languages

In biology and chemistry a standard proceeding is to conduct an experiment, observe its progress, andthen take the result of this observation as the 1nal output. Inspiredby this, we have introduced P/O systems (A. Alhazov, C. Mart5 6n-Vide, Gh. P9 aun, Pre-Proc. of the Workshop on Membrane Computing 2003, Tarrragona, Spain; http://pizarro. ces to generate any recursively enumerable language. In a thirdcase, we obtain a class of languages between the context-free andcontext-sensitive ones. c 2004 Elsevier B.V. All rights reserved.

Evolution and Observation: A New Way to Look at Membrane Systems

An architecture for investigating the dynamical behaviour of biological systems is proposed by using the concepts of behaviour and observer. The behaviour of a biological system is the sequence of states traversed as time passes; the observer is a device translating this behaviour into a readable output. As an instance of this architecture we investigate P/O systems constituted by a membrane system and a multiset finite automaton observer. We first characterize the infinite behaviours of conservative systems, i.e., systems whose number of objects is constant. These systems behave very regularly. For more sophisticated systems we then use also more complicated multiset automata as observers: they map the configurations into an output alphabet and thus we obtain words describing the entire computations. Even for seemingly simple membrane systems using only non-cooperative rules and regular-like observers through this combination a great power emerges, in our case computational universality.

On the size complexity of hybrid networks of evolutionary processors

The goal of this paper is twofold. Firstly, to survey in a systematic and uniform way the main results regarding the size descriptional complexity measures of hybrid networks of evolutionary processors as generating devices. Secondly, we improve some results about a size measure, prove that it is connected, and discuss the possibility of computing this measure for regular and context-free languages. We also briefly present a few NP-complete problems and recall how they can be solved in linear time by accepting networks of evolutionary processors with linearly bounded resources (nodes, rules, symbols). Finally, the size complexity of accepting hybrid networks of evolutionary processors recognizing all NP languages in polynomial time is briefly discussed.

Uniformly bounded duplication languages

We consider a new type of language defined by a word through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate the effect of restricting the factor length to a constant. We prove that all these languages are regular, any word has a unique uniformly bounded duplication root, and show how this root can be computed in linear time and memory. We also address the problem of computing the uniformly bounded duplication distance between two words.

Bounded hairpin completion

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.

Formal Languages Arising from Gene Repeated Duplication

We consider two types of languages defined by a string through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate some decidability matters concerning the unbounded duplication languages and then fix the place of bounded duplication languages in the Chomsky hierarchy by showing that all these languages are context-free. We give some conditions for the non-regularity of these languages. Finally, we discuss some open problems and directions for further research.

5′ → 3′ Watson-Crick Automata With Several Runs

5′ → 3′ WK-automata are Watson-Crick automata whose two heads start on opposite ends of the input word and always run in opposite directions. One full reading in both directions is called a run. We prove that the expressive power of these automata increases with every additional run that they can make, both for deterministic and non-deterministic machines. This defines two incomparable infinite hierarchies of language classes between the regular and the context-sensitive languages. These hierarchies are complemented with classes defined by several restricted variants of 5′ → 3′ WK-automata like stateless automata. Finally we show that several standard problems are undecidable for languages accepted by 5′ → 3′ WK-automata in only one run, for example the emptiness and the finiteness problems.

Roots and powers of regular languages

For a set H of natural numbers, the H-power of a language L is the set of all words pk where p ∈ L and k ∈ H. The root of L is the set of all primitive words p such that pn belongs to L for some n ≥ 1. There is a strong connection between the root and the powers of a regular language L namely, the H-power of L for an arbitrary finite set H with 0, 1, 2 ∉ H is regular if and only if the root of L is finite. If the root is infinite then the H-power for most regular sets H is context-sensitive but not context-free. The stated property is decidable.

DNA splicing: computing by observing

Motivated by several techniques for observing molecular processes in real-time we introduce a computing device that stresses the role of the observer in biological computations and that is based on the observed behavior of a splicing system. The basic idea is to introduce a marked DNA strand into a test tube with other DNA strands and restriction enzymes. Under the action of these enzymes the DNA starts to splice. An external observer monitors and registers the evolution of the marked DNA strand. The input marked DNA strand is then accepted if its observed evolution follows a certain expected pattern. We prove that using simple observers (finite automata), applied on finite splicing systems (finite set of rules and finite set of axioms), the class of recursively enumerable languages can be recognized.

Evolution and observation: a non-standard way to accept formal languages

It is a very common procedure in biology to observe the progress of an experiment and regard the result of this observation as the final outcome. Inspired by this, a new approach for generating formal languages, called evolution/observation, has been introduced [6]. In the current work we consider evolution/observation as a new strategy also for accepting languages: a word is accepted, if the (observed) evolution of a certain system starting from this input follows a regular pattern. We obtain the following result: checking if the (observed) evolution of a context-free system follows a regular pattern is enough to accept every recursively enumerable languages. On the other hand, if we observe the evolution of systems using very simple rules (of the kind a → b), then it is possible to accept exactly the class of context-sensitive languages.