International Journal of Foundations of Computer Science

We present a formal model inspired by the epigenetic process of gene annotation via histone modification. In particular, we study the generative capacity of a system in which annotations on a set of strings control which substrings are ultimately produced by the system and in which only the annotations, and not the strings themselves, may be rewritten. On a biological level this represents a first attempt to better understand the computational limits of this form of epigenetic regulation. We introduce two different derivation modes for our formal system and show that these systems are actually quite weak. The weaker of the derivation modes is directly capable only of generating a subset of the regular languages while the more powerful derivation mode is also only capable of generating all regular languages modulo a begin- and an end-marker.

We are interested in the state complexity of languages that are defined via the subword closure operation. The subword closure of a set S of fixed-length words is the set of all words w for which any subword of w of the fixed length is in S. This type of constraint appears to be useful in various situations related to data encodings and in particular to DNA encodings. We present a few results related to this concept. In particular we give a general upper bound on the state complexity of a subword closed language and show that this bound is tight infinitely often. We also discuss the state complexity of DNA computing related cases of the subword closure operation.

In this paper we consider, from the descriptional complexity point of view, a model of computation introduced in [1], namely accepting network of evolutionary processors with filtered connections (ANEPFCs). First we show that for each morphism h : V → W*, with V ∩ W = ∅, one can effectively construct an ANEPFC, of size 6 + |W|, which accepts every input word w and, at the end of the computation on this word, obtains h(w) in its output node. This result can be applied in constructing two different ANEPFCs, with 27 and, respectively, 26 processors, recognizing a given recursively enumerable language. The first architecture, based on the construction of a universal ANEPFC, has the property that only 7 of its 27 processors depend on the accepted language. On the other hand, all the 26 processors of the second architecture depend on the accepted language, but, differently from the first one, this network simulates efficiently (from both time and space perspectives) a nondeterministic Turing machine accepting the given language.

We propose two different ways to simulate Boolean circuits in the framework of ciliate computations, based on the intramolecular and on the intermolecular gene assembly models with contextual operations applied in a maximal parallel manner. In both cases, the running time and the size of resources of the simulating devices are proportional to the corresponding depth and size of the simulated Boolean circuits.

Computer modeling of molecular signaling cascades can provide useful insight into the underlying complexities of biological systems. We present a refined approach for the discrete modeling of protein interactions within the environment of a single cell. The technique we offer utilizes the Membrane Systems paradigm which, due to its hierarchical structure, lends itself readily to mimic the behavior of cells. Since our approach is nondeterministic and discrete, it provides an interesting contrast to the standard deterministic ordinary differential equations techniques. We argue that our approach may outperform ordinary differential equations when modeling systems with relatively low numbers of molecules – a frequent occurrence in cellular signaling cascades.

Refinements over our previous modeling efforts include the addition of nondeterminism for handling reaction competition over limited reactants, increased efficiency in the storing and sorting of reaction waiting times, and modifications of the model reactions. Results of our discrete simulation of the type I and type II Fas-mediated apoptotic signaling cascade are illustrated and compared with two approaches: one based on ordinary differential equations and another based on the well-known Gillespie algorithm.

DNA strands that, mathematically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: If some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper studies a mathematical formalization of a particular case of hairpins, the Watson-Crick bordered words. A Watson-Crick bordered word is a word with the property that it has a prefix that is Watson-Crick complementary to its suffix. We namely study algebraic properties of Watson-Crick bordered and unbordered words. We also give a complete characterization of the syntactic monoid of the language consisting of all Watson-Crick bordered words over a given alphabet. Our results hold for the more general case where the Watson-Crick complement function is replaced by an arbitrary antimorphic involution.

We consider the problem of synchronizing the activity of all the membranes of a P system. After pointing at the connection with a similar problem dealt with in the field of cellular automata where the problem is called the firing squad synchronization problem, FSSP for short, we provide two algorithms to solve this problem. One algorithm is non-deterministic and it works in the time 3h, where h is the height of the tree defining the membrane structure of the considered P system. The other algorithm is deterministic and it works in time 4n + 2h, where n is the number of membranes of the considered P system. Finally, we suggest various directions to continue this work.

We study a modelling framework and computational paradigm called Colonies of Synchronizing Agents (CSAs), which abstracts intracellular and intercellular mechanisms of biological tissues. The model is based on a multiset of agents (cells) in a common environment (a tissue). Each agent has a local contents, stored in the form of a multiset of atomic objects (e.g., representing molecules), updated by multiset rewriting rules which may act on individual agents (intracellular action) or synchronize the contents of pairs of agents (intercellular action).

In this paper we investigate dynamic properties of CSAs, by means of temporal logic, and we give a logical characterization of some notions inspired by biology such as robustness, mutants and species. We reveal the relation that exists between the concept of robustness for CSAs and the bisimulation relation on colonies. We also present some decidability results for particular cases of robustness.

We consider extended variants of spiking neural P systems with decaying spikes (i.e., the spikes have a limited lifetime) and/or total spiking (i.e., the whole contents of a neuron is erased when it spikes). Although we use the extended model of spiking neural P systems, these restrictions of decaying spikes and/or total spiking do not allow for the generation or the acceptance of more than regular sets of natural numbers.

In this paper, we look at the extension of Hedlund's characterization of cellular automata to the case of cellular automata in the hyperbolic plane. This requires an additional condition. The new theorem is proved with full details in the case of the pentagrid and in the case of the ternary heptagrid and enough indications to show that it also holds on the grids {p, q} of the hyperbolic plane.

We introduce the notion of stateless multihead two-way (respectively, one-way) NFAs and stateless multicounter systems and relate them to P systems and vector addition systems. In particular, we investigate the decidability of the emptiness and reachability problems for these stateless automata and show that the results are applicable to similar questions concerning certain variants of P systems, namely, token systems and sequential tissue-like P systems.