International Journal of Foundations of Computer Science

In this paper we consider universal systems based on splicing. As in previous works, we take the number of rules as the parameter for the descriptional complexity. We present three results: universal double splicing extended H system with 5 rules, universal splicing test tube system with 8 rules and a universal splicing P system with 5 rules.

The classical decision problem associated with a game is whether a given player has a winning strategy, i.e. some strategy that leads almost surely to a victory, regardless of the other players' strategies. While this problem is relevant for deterministic fully observable games, for a partially observable game the requirement of winning with probability 1 is too strong. In fact, as shown in this paper, a game might be decidable for the simple criterion of almost sure victory, whereas optimal play (even in an approximate sense) is not computable.

We therefore propose another criterion, the decidability of which is equivalent to the computability of approximately optimal play. Then, we show that (i) this criterion is undecidable in the general case, even with deterministic games (no random part in the game), (ii) that it is in the jump 0', and that, even in the stochastic case, (iii) it becomes decidable if we add the requirement that the game halts almost surely whatever maybe the strategies of the players.

We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems.

In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

In this paper, we study to what extent decidability is connected to universality. A natural context for such a study is provided by the axiomatic theory of computability, automata and algorithms. In Section 2, we introduce necessary concepts, constructions, axioms, postulates, conditions and problems. Section 3 contains the main results of the paper. In particular, it is demonstrated (Theorems 1 and 2) that undecidability of algorithmic problems does not depend on existence of universal algorithms and may be caused by weaker conditions. At the same time, results of Theorems 2 and 3 demonstrate that decidability is incompatible with universality. It is also proved (Theorem 5) that sufficiently big classes of total algorithms/automata, such as the class of all primitive recursive functions, cannot have universal algorithms/automata.

It was noticed by Harel in [Har86] that "one can define -complete versions of the well-known Post Correspondence Problem". We first give a complete proof of this result, showing that the infinite Post Correspondence Problem in a regular ω-language is -complete, hence located beyond the arithmetical hierarchy and highly undecidable. We infer from this result that it is -complete to determine whether two given infinitary rational relations are disjoint. Then we prove that there is an amazing gap between two decision problems about ω-rational functions realized by finite state Büchi transducers. Indeed Prieur proved in [Pri01, Pri02] that it is decidable whether a given ω-rational function is continuous, while we show here that it is -complete to determine whether a given ω-rational function has at least one point of continuity. Next we prove that it is -complete to determine whether the continuity set of a given ω-rational function is ω-regular. This gives the exact complexity of two problems which were shown to be undecidable in [CFS08].

A classical theme in recursion theory is the question whether for a set A and n given elements x₁,…,x_n, an oracle machine having access to an oracle B can determine which of the elements x_i belong to A. And if yes, how many queries are necessary? Here, B = A is possible and leads to interesting special cases of the general question

In the present paper we adapt classical notions in this area of bounded query computations to real number algorithms as formalized by Blum, Shub, and Smale and analyze them in the new framework. Among the results obtained we find: A real version of a non-speedup theorem based on real quantifier elimination, some basic properties about selective real sets, and a way to construct natural terse sets in ℝ by applying the implicit function theorem. The purpose of the paper is on presenting some interesting questions and basic results as an appertizer to intensify research into this direction.

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problems, which models many real-life problems. However, it is considered as one of the most difficult NP-hard problems, which means that no polynomial-time algorithm is known to solve this intractable problem effectively. Even small instances of QAP may require vast computation time. In this work, a uniform cellular solution to QAP is proposed in the framework of membrane computing by using a family of recognizer tissue P systems with cell division. In the design of the solution, we encode the given instances in binary notations. The paper can be considered as a contribution to the study of considering a binary encoding of the information in P systems.

This paper deals with the problem of distributed causal model-based diagnosis on interacting Behavioral Petri Nets (BPNs). The system to be diagnosed comprises different interacting subsystems (each modeled as a BPN) and the diagnostic system is defined as a multi-agent system where each agent is designed to diagnose a particular subsystem on the basis of its local model, the local received observation and the information exchanged with the neighboring agents. The interactions between subsystems are captured by tokens that may pass from one net model to another via bordered places. The diagnostic reasoning scheme is accomplished locally within each agent by analyzing the P-invariants of the corresponding BPN model. Once local diagnoses are obtained, agents begin to communicate to ensure that such diagnoses are consistent and recover completely the results obtained by a centralized agent having a global view about the whole system.

The spanning star forest problem is an interesting algorithmic problem in combinatorial optimization and finds different applications. We generalize it into the spanning k-tree forest problem, which is to find a maximum spanning forest in which each tree component has a central vertex and other vertices in the component have distance at most k away from the central vertex. We show that this new problem can be approximated with ratio in polynomial time for both undirected and directed graphs. In the weighted distance model, a ½-approximation algorithm is presented for it.

The present paper proposes a new investigation area in automata theory — jumping finite automata. These automata work like classical finite automata except that they read input words discontinuously — that is, after reading a symbol, they can jump over some symbols within the words and continue their computation from there. The paper establishes several results concerning jumping finite automata in terms of commonly investigated areas of automata theory, such as decidability and closure properties. Most importantly, it achieves several results that demonstrate differences between jumping finite automata and classical finite automata. In its conclusion, the paper formulates several open problems and suggests future investigation areas.