Sergiu Ivanov

Random Context and Semi-conditional Insertion-deletion Systems

In this article we introduce the operations of insertion and deletion working in random context and semi-conditional modes. We show that conditional application of insertion and deletion rules strictly increases the computational power. In the case of semi-conditional insertion-deletion systems, context-free insertion and deletion rules of one symbol are sufficient to achieve computational completeness. In the random context case, our results expose asymmetry between the computational power of insertion and deletion rules: semi-conditional systems of size 2, 0, 0; 1, 1, 0 with context-free two-symbol insertion rules, and one-symbol deletion rules with one-symbol left context are computationally complete, while systems of size 1, 1, 0; 2, 0, 0 and, more generally, of size 1, 1, 0; p, 1, 1 are not.

Complexity of model checking for reaction systems

Reaction systems are a new mathematical formalism inspired by the living cell and driven by only two basic mechanisms: facilitation and inhibition. As a modeling framework, they differ from the traditional approaches based on ODEs and CTMCs in two fundamental aspects: their qualitative character and the non-permanency of resources. In this article we introduce to reaction systems several notions of central interest in biomodeling: mass conservation, invariants, steady states, stationary processes, elementary fluxes, and periodicity. We prove that the decision problems related to these properties span a number of complexity classes from P to NP- and coNP-complete to PSPACE-complete.

Small Universal Non-deterministic Petri Nets with Inhibitor Arcs

This paper investigates the universality problem for Petri nets with inhibitor arcs. Four descriptional complexity parameters are considered: the number of places, transitions, inhibitor arcs, and the maximal degree of a transition. Each of these parameters is aimed to be minimized, a special attention being given to the number of places. Four constructions are presented having the following values of parameters (listed in the above order): (5, 877, 1022, 729), (5, 1024, 1316, 379), (4, 668, 778, 555), and (4, 780, 1002, 299). The decrease of the number of places with respect to previous work is primarily due to the consideration of non-deterministic computations in Petri nets. Using equivalencies between models our results can be translated to multiset rewriting with forbidding conditions, or to P systems with inhibitors.

Dependency graphs and mass conservation in reaction systems

Reaction systems is a new mathematical formalism inspired by the biological cell, which focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. In this article we focus on the property of mass conservation for reaction systems. We show that conservation of sets gives rise to a relation between the species, which we capture in the concept of the conservation dependency graph. We then describe an application of this relation to the problem of listing all conserved sets. We further give a sufficient negative polynomial criterion which can be used for proving that a set is not conserved. Finally, we present a simulator of reaction systems, which also includes an implementation of the algorithm for listing the conserved sets of a given reaction system.

About One-Sided One-Symbol Insertion-Deletion P Systems

In this article we consider insertion-deletion P systems inserting or deleting one symbol in one or two symbol(s) left context (more precisely of size (1,2,0;1,1,0) and (1,1,0;1,2,0)). We show that computational completeness can be achieved by using only 3 membranes in a tree-like structure. Hence we obtain a trade-off between the sizes of contexts of insertion and deletion rules and the number of membranes sufficient for computational completeness.

Universality of Graph-controlled Leftist Insertion-deletion Systems with Two States

In this article, we consider leftist insertion-deletion systems, in which all rules have contexts on the same side, and may only insert or delete one symbol at a time. We start by introducing extended rules, in which the contexts may be specified as regular expressions, instead of fixed words. We then prove that leftist systems with such extended rules and two-state graph control can simulate any arbitrary 2-tag system. Finally, we show how our construction can be simulated in its turn by graph-controlled leftist insertion-deletion systems with conventional rules of sizes (1, 1, 0; 1, 2, 0) and (1, 2, 0; 1, 1, 0) (where the first three numbers represent the maximal size of the inserted string and the maximal size of the left and right contexts respectively, while the last three numbers provide the same information about deletion rules), which implies that the latter systems are universal.

Forward and Backward Chaining with P Systems

One of the concepts that lie at the basis of membrane computing is the multiset rewriting rule. On the other hand, the paradigm of rules is profusely used in computer science for representing and dealing with knowledge. Therefore, establishing a “bridge†between these domains is important, for instance, by designing P systems reproducing the modus ponens-based forward and backward chaining that can be used as tools for reasoning in propositional logic. In this paper, the authors show how powerful and intuitive the formalism of membrane computing is and how it can be used to represent concepts and notions from unrelated areas.

Contextual array grammars with matrix control, regular control languages, and tissue P systems control

We consider d-dimensional contextual array grammars and investigate their computational power when using various control mechanisms – matrices, regular control languages, and tissue P systems, which work like regular control languages, but may end up with a final check for the non-applicability of some rules. For d≥2, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages. The use of tissue P systems with their final non-applicability check even yields some additional computational power. In the 1-dimensional case, the family of 1-dimensional array languages generated by contextual array grammars with regular control languages can be characterized as the family of array images of the linear languages, which for a one-letter alphabet means that it coincides with the family of regular 1-dimensional array languages.

Simulating R Systems by P Systems

We show multiple ways of how to simulate R systems by non-cooperative P systems with atomic control by promoters and/or inhibitors, or with matter/antimatter annihilation rules, with a slowdown by a constant factor only. The descriptional complexity of the simulating P systems is also linear with respect to that of the simulated R system. All constants depend on how general the model of R systems is, as well as on the chosen control ingredients of the P systems. Special attention is paid to the differences in the mode of rule application in these models.

P Systems with Generalized Multisets Over Totally Ordered Abelian Groups

In this paper we extend the definition of a multiset by allowing elements to have multiplicities from an arbitrary totally ordered Abelian group instead of only using natural numbers. We consider P systems with such generalized multisets and give well-founded notations for the applicability of rules and for different derivation modes. These new definitions raise challenging mathematical questions and we propose several solutions yielding models sometimes having quite unexpected behavior. Another interesting application of our results is the possibility to consider complex objects and to manipulate them directly in a P system instead of their numerical encodings.