Lila Kari

The many facets of natural computing

Natural computing builds a bridge between computer science and natural sciences.

Computationally universal P systems without priorities: two catalysts are sufficient

The original model of P systems with symbol objects introduced by Paun was shown to be computationally universal, provided that catalysts and priorities of rules are used. By reduction via register machines Sosik and Freund proved that the priorities may be omitted from the model without loss of computational power. Freund, Oswald, and Sosik considered several variants of P systems with catalysts (but without priorities) and investigated the number of catalysts needed for these specific variants to be computationally universal. It was shown that for the classic model of P systems with the minimal number of two membranes the number of catalysts can be reduced from six to five; using the idea of final states the number of catalysts could even be reduced to four. In this paper we are able to reduce the number of catalysts again: two catalysts are already sufficient. For extended P systems we even need only one membrane and two catalysts. For the (purely) catalytic systems considered by Ibarra only three catalysts are already enough.

Contextual Insertions/Deletions and Computability

We investigate two generalizations of insertion and deletion of words, that have recently become of interest in the context of molecular computing. Given a pair of words (x, y), called a context, the (x, y)-contextual insertion of a wordvinto a worduis performed as follows. For each occurrence ofxyas a subword inu, we include in the result of the contextual insertion the words obtained by insertingvintou, betweenxandy. The (x, y)-contextual deletion operation is defined in a similar way. We study closure properties of the Chomsky families under the defined operations, contextual ins-closed and del-closed languages, and decidability of existence of solutions to equations involving these operations. Moreover, we prove that every Turing machine can be simulated by a system based entirely on contextual insertions and deletions

DNA computing, sticker systems, and universality

Abstract. We introduce the sticker systems, a computability model, which is an abstraction of the computations using the Watson-Crick complementarity as in Adlemans DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence the power of finite automata. One variant is proven to be equivalent to Turing machines. Another one is found to have a strictly intermediate power.

Universal Molecular Computation in Ciliates

How do cells and nature “compute”? They read and “rewrite” DNA all the time, by processes that modify sequences at the DNA or RNA level. In 1994, Adleman’s elegant solution to a seven-city Directed Hamiltonian Path problem using DNA [1] launched the new field of DNA computing, which in a few years has grown to international scope. However, unknown to this field, ciliated protozoans of genus Oxytricha and Stylonychia had solved a potentially harder problem using DNA several million years earlier. The solution to this “problem”, which occurs during the process of gene unscrambling, represents one of nature’s ingenious solutions to the problem of the creation of genes. Here we develop a model for the guided homologous recombinations that take place during gene rearrangement and prove that such a model has the computational power of a Turing machine, the accepted formal model of computation. This indicates that, in principle, these unicellular organisms may have the capacity to perform at least any computation carried out by an electronic computer.

On language equations with invertible operations

The paper studies language equations of the type X ? L = R and L ? Y = R, where L and R are given languages and ? is an invertible binary word (language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R is a regular one, the existence of a solution is generally undecidable. The results can be extended to more complex linear equations, systems of linear equations as well as for equations of higher degree.

Coding properties of DNA languages

The computation language of a DNA-based system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in DNA computations. We give several characterizations of the desired properties and provide methods for obtaining languages with such properties. The decidability of these properties is addressed as well. As an application we consider splicing systems whose computation language is free of certain undesirable bonds and is generated by nearly optimal comma-free codes.

Sticky-free and overhang-free DNA languages

Abstract.An essential step of any DNA computation is encoding the input data on single or double DNA strands. Due to the biochemical properties of DNA, complementary single strands can bind to one another forming double-stranded DNA. Consequently, data-encoding DNA strands can sometimes interact in undesirable ways when used in computations. It is crucial thus to analyze properties that guard against such phenomena and study sets of sequences that ensure that no unwanted bindings occur during any computation. This paper formalizes and investigates properties of DNA languages that guarantee their robusteness during computations. After defining and investigating several types of DNA languages possessing good encoding properties, such as sticky-free and overhang-free languages, we give algorithms for deciding whether regular DNA languages are invariant under bio-operations. We also give a method for constructing DNA languages that, in addition to being invariant and sticky-free, possess error-detecting properties. Finally, we present the results of running tests that check whether several known gene languages (the set of genes of a given organism) as well as the input DNA languages used in Adleman’s DNA computing experiment, have the defined properties.

Codes, involutions, and DNA encodings

DNA computing as a field started in 1994 when Leonard Adleman solved a hard computational problem entirely by manipulations of DNA molecules in a test tube [1]. The premise behind DNA computing is that DNA is capable of storing information, while various laboratory techniques that operate on and modify DNA strands (called bio-operations in the sequel) can be used to perform computational steps. Most DNA computations consists of three basic stages. The first is encoding the problem using single-stranded or double-stranded DNA. Then the actual computation is performed by employing a succession of bio-operations [14]. Finally, the DNA strands representing the solution to the problem are detected and decoded. Because of the nature of the substrate in which the data is encoded, namely DNA strands, problems can occur at the encoding stage which would not occur in an electronic medium. In order to describe these problems and our attempts at solutions, we now briefly present some basic molecular biology notions and notations.

On properties of bond-free DNA languages

The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a double-stranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.