Artiom Alhazov

Further remarks on P systems with active membranes, separation, merging, and release rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and confluent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, T.-O. Isdorj. A universality result related to membrane separation is also obtained.

P systems with minimal insertion and deletion

In this paper, we consider insertion-deletion P systems with priority of deletion over insertion. We show that such systems with one-symbol context-free insertion and deletion rules are able to generate Parikh sets of all recursively enumerable languages (PsRE). If a one-symbol one-sided context is added to the insertion or deletion rules, then all recursively enumerable languages can be generated. The same result holds if a deletion of two symbols is permitted. We also show that the priority relation is very important, and in its absence the corresponding class of P systems is strictly included in the family of matrix languages (MAT).

On reversibility and determinism in p systems

Membrane computing is a formal framework of distributed parallel computing. In this paper we study the reversibility and maximal parallelism of P systems from the computability point of view. The notions of reversible and strongly reversible systems are considered. The universality is shown for reversible P systems with either priorities or inhibitors, and a negative conjecture is stated for reversible P systems without such control. Strongly reversible P systems without control have shown to only generate sub-finite sets of numbers; this limitation does not hold if inhibitors are used. n nAnother concept considered is strong determinism, which is a syntactic property, as opposed to the determinism typically considered in membrane computing. Strongly deterministic P systems without control only accept sub-regular sets of numbers, while systems with promoters and inhibitors are universal.

Sequential and maximally parallel multiset rewriting: reversibility and determinism

We study reversibility and determinism aspects and the strong versions of these properties of sequential multiset processing systems and of maximally parallel systems, from the computability point of view. In the sequential case, syntactic criteria are established for both strong determinism and strong reversibility. In the parallel case, a criterion is established for strong determinism, whereas strong reversibility is shown to be decidable. In the sequential case, without control all four classes—deterministic, strongly deterministic, reversible, strongly reversible—are not universal, whereas in the parallel case deterministic systems are universal. When allowing inhibitors, the first and the third class become universal in both models, whereas with priorities all of them are universal. In the maximally parallel case, strongly deterministic systems with both promoters and inhibitors are universal. We also present a few more specific results and conjectures.

Universality of 2-State 3-Symbol Reversible Logic Elements — A Direct Simulation Method of a Rotary Element

A reversible logic element is a primitive from which reversible computing systems can be constructed. A rotary element is a typical 2-state 4-symbol reversible element with logical universality, and we can construct reversible Turing machines from it very simply. There are also many other reversible element with 1-bit memory. So far, it is known that all the 14 kinds of non-degenerate 2-state 3-symbol reversible elements can simulate a Fredkin gate, and hence they are universal. In this paper, we show that all these 14 elements can “directly” simulate a rotary element in a simple and systematic way.

A sequence-based analysis of the pointer distribution of stichotrichous ciliates

Micronuclear genes in stichotrichous ciliates are broken into blocks separated by noncoding sequences, sometimes with the blocks in a shuffled order, some even inverted. During reproduction, all blocks are assembled in the correct order and orientation. This process is possible due to the special structure of micronuclear genes: each coding block M ends with a short nucleotide sequence (called pointer) that is repeated at the beginning of the coding block that should follow M in the assembled gene. Many of the pointers have multiple occurrences along both strands of the gene. This yields a very high number of pointer-induced possible divisions into coding and noncoding blocks. We investigate the distribution of pointers for all currently sequenced micronuclear ciliate genes with the goal of identifying what distinguishes the real gene structure among all possible coding/noncoding divisions. We find a sharp criterion in the average a/t-content of the noncoding blocks: the real division has, in most cases, the maximum such content among all possible combinations. Even for pointers as short as two nucleotides, the real division is one of very few with an average a/t-content of its noncoding blocks over 80%. The separation is most clear when the loci of pointers of up to four nucleotides (even three in the case of unscrambled genes) are fixed (e.g., through a template-based recombination mechanism).

Reversibility and determinism in sequential multiset rewriting

We study reversibility and determinism aspects of sequential multiset processing systems, and the strong versions of these properties. n nSyntactic criteria are established for both strong determinism and for strong reversibility. It also shown that without control all four classes -deterministic, strongly deterministic, reversible, strongly reversibleare not universal, while allowing priorities or inhibitors the first and the third class become universal. Moreover, strongly deterministic multiset rewriting systems with priorities are also universal.

Hierarchical P Systems with Randomized Right-Hand Sides of Rules

P systems are a model of hierarchically compartmentalized multiset rewriting. We introduce a novel kind of P systems in which rules are dynamically constructed in each step by non-deterministic pairing of left-hand and right-hand sides. We define three variants of right-hand side randomization and compare each of them with the power of conventional P systems. It turns out that all three variants enable non-cooperative P systems to generate exponential (and thus non-semi-linear) number languages. We also give a binary normal form for one of the variants of P systems with randomized rule right-hand sides.

On universality of radius 1/2 number-conserving cellular automata

A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modeling of the physical conservation laws of mass or energy. In this paper we show a construction method of radius 1/2 NCCAs. The local transition function is expressed via a single unary function which can be regarded as flows of numbers. In spite of the strong constraint, we constructed radius 1/2 NCCAs that simulate any radius 1/2 cellular automata or any radius 1 NCCA. We also consider the state complexity of these non-splitting simulations (4n2 + 2n + 1 and 8n2 + 12n - 16, respectively). These results also imply existence of an intrinsically universal radius 1/2 NCCA.

Simulating Evolutional Symport/Antiport by Evolution-Communication and vice versa in Tissue P Systems with Parallel Communication

We aim to compare functionality of symport/antiport with embedded rewriting to that of symport/antiport accompanied by rewriting, by two-way simulation, in case of tissue P systems with parallel communication. A simulation in both directions with constant slowdown is constructed.