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The unification problem for term rewriting systems (TRSs) is the problem of deciding, for a given TRS R and two terms M and N, whether there exists a substitution θ such that Mθ and Nθ are congruent modulo R (i.e., Mθ↔R*Nθ). In this paper, the unification problem for confluent right-ground TRSs is shown to be decidable. To show this, the notion of minimal terms is introduced and a new unification algorithm for obtaining a substitution whose range consists of minimal terms is proposed. Our result extends the decidability of unification for canonical (i.e., terminating and confluent) right-ground TRSs given by Hullot [Proceedings of the 5th Conference on Automated Deduction, LNCS, vol. 87, 1980, p. 318] in the sense that the termination condition can be omitted. [Copyright &y& Elsevier]

In this paper we consider an approach to passive learning. In contrast to the classical PAC model we do not assume that the examples are independently drawn according to an underlying distribution, but that they are generated by a time-driven process. We define deterministic and probabilistic learning models of this sort and investigate the relationships between them and with other models. The fact that successive examples are related can often be used to gain additional information similar to the information gained by membership queries. We show how this can be used to design on-line prediction algorithms. In particular, we present efficient algorithms for exactly identifying Boolean threshold functions and 2-term RSE, and for learning 2-term-DNF, when the examples are generated by a random walk on {0,1}n. [Copyright &y& Elsevier]

Some computationally hard problems, e.g., deduction in logical knowledge bases– are such that part of an instance is known well before the rest of it, and remains the same for several subsequent instances of the problem. In these cases, it is useful to preprocess off-line this known part so as to simplify the remaining on-line problem. In this paper we investigate such a technique in the context of intractable, i.e., NP-hard, problems. Recent results in the literature show that not all NP-hard problems behave in the same way: for some of them preprocessing yields polynomial-time on-line simplified problems (we call them compilable), while for other ones their compilability implies some consequences that are considered unlikely. Our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable. To this end, we define new models of computation, complexity classes, and reductions. We find complete problems for such classes, “completeness” meaning they are “the less likely to be compilable.” We also investigate preprocessing that does not yield polynomial-time on-line algorithms, but generically “decreases” complexity. This leads us to define “hierarchies of compilability,” that are the analog of the polynomial hierarchy. A detailed comparison of our framework to the idea of “parameterized tractability” shows the differences between the two approaches. [Copyright &y& Elsevier]

Parameterized verification of coverability in broadcast networks with finite state processes has been studied for different types of models and topologies. In this paper, we attempt to develop a theory of broadcast networks in which the processes can be well-structured transition systems. The resulting formalism is called well-structured broadcast networks. For various types of communication topologies, we prove the decidability of coverability in the static case, i.e., when the network topology is not allowed to change. We do this by showing that for these types of static communication topologies, the broadcast network itself is a well-structured transition system , hence proving the decidability of coverability in the broadcast network. We also give an algorithm to decide coverability of well-structured broadcast networks when reconfiguration of links between nodes is allowed. Finally, with minor modifications of this algorithm we prove decidability of coverability when the underlying process is a pushdown automaton. [ABSTRACT FROM AUTHOR]

Image matching is an important task arising in video compression, optical character recognition, medical imaging, watermarking and in many others fields. Given two digital images A and B , image matching determines a transformation f for A such that it most closely resembles B. In this paper, we introduce the first general discretization technique that works for the class of projective transformations as well as plenty of its subclasses such as affine transformations and several combinations of scaling, rotation and translation. Based on this, we provide a fully generic image matching algorithm for all these classes that runs in polynomial time. [ABSTRACT FROM AUTHOR]

The PQ-tree is a fundamental data structure that has also been used in comparative genomics to model ancestral genomes with some uncertainty. To quantify the evolution between genomes represented by PQ-trees, in this paper we study two fundamental problems of PQ-tree comparison motivated by this application. First, we show that the problem of comparing two PQ-trees by computing the minimum breakpoint distance among all pairs of permutations generated respectively by the two considered PQ-trees is NP-complete for unsigned permutations. Next, we consider a generalization of the classical Breakpoint Median problem, where an ancestral genome is represented by a PQ-tree and p ≥ 1 permutations are given and we want to compute a permutation generated by the PQ-tree that minimizes the sum of the breakpoint distances to the p permutations (or k). We show that this problem is also NP-complete for p ≥ 2 , and is fixed-parameter tractable with respect to k for p ≥ 1. [ABSTRACT FROM AUTHOR]

The McNaughton-Zielonka divide et impera algorithm is the simplest and most flexible approach available in the literature for determining the winner in a parity game. Despite its theoretical exponential worst-case complexity and the negative reputation as a poorly effective algorithm in practice, it has been shown to rank among the best techniques for solving such games. Also, it proved to be resistant to a lower bound attack, even more than the strategy improvements approaches, but finally Friedmann provided a family of games on which the algorithm requires exponential time. An easy analysis of this family shows that a simple memoization technique can help the algorithm solve the family in polynomial time. The same result can also be achieved by exploiting an approach based on the dominion-decomposition techniques proposed in the literature. These observations raise the question whether a suitable combination of dynamic programming and game-decomposition techniques can improve on the exponential worst case of the original algorithm. In this paper we answer this question negatively, by providing a robustly exponential worst case, showing that no possible intertwining of the above mentioned techniques can help mitigating the exponential nature of the divide et impera approaches. The resulting worst case is even more robust than that, since it serves as a lower bound for progress measures based algorithms as well, such as Small Progress Measure and its quasi-polynomial variant recently proposed by Jurdziński and Lazic. [ABSTRACT FROM AUTHOR]