Well-structured transition systems (WSTS's) are a general class of infinite state systems for which decidability results rely on the existence of a well-quasi-ordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved definitions allow many examples of classical systems to be seen as instances of WSTS's.

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In applications dealing with ordered domains, the available data is frequently indefinite. While the domain is actually linearly ordered, only some of the order relations holding between points in the data are known. Thus, the data provides only a partial order, and query answering involves determining what holds under all the compatible linear orders. In this paper we study the complexity of evaluating queries in logical databases containing such indefinite information. We show that in this context queries are intractable even under the data complexity measure, but identify a number of PTIME sub-problems. Data complexity in the case of monadic predicates is one of these PTIME cases, but for disjunctive queries the proof is non-constructive, using well-quasi-order techniques. We also show that the query problem we study is equivalent to the problem of containment of conjunctive relational database queries containing inequalities. One of our results implies that the latter is \Pi p 2 ...

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Partial evaluation is a method for program specialization based on fold/unfold transformations [8, 25]. Partial evaluation of pure functional programs uses mainly static values of given data to specialize the program [15, 44]. In logic programming, the so-called static/dynamic distinction is hardly present, whereas considerations of determinacy and choice points are far more important for control [12]. We discuss these issues in the context of a (lazy) functional logic language. We formalize a two-phase specialization method for a non-strict, first order, integrated language which makes use of lazy narrowing to specialize the program w.r.t. a goal. The basic algorithm (first phase) is formalized as an instance of the framework for the partial evaluation of functional logic programs of [2, 3], using lazy narrowing. However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy. A post-processing renaming scheme (second phase) is necessary which we describe and illustrate on the well-known matching example. This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies. We show that our method preserves the lazy narrowing semantics and that the inclusion of simplification steps in narrowing derivations can improve control during specialization.

this paper. In particular, their comments inspired and gave arguments for the discussion on the value of the classical decision problem after Church's and Turing's results. References

A partition u of [k] = f1; 2; : : : ; kg is contained in another partition v of [l] if [l] has a k-subset on which v induces u. We are interested in counting partitions v not containing a given partition u or a given set of partitions R. This concept is related to that of forbidden permutations. A strengthening of Stanley--Wilf conjecture is proposed.

Abstract. In order to make multithreaded programming manageable, programmers often follow a design principle where they break the problem into tasks which are then solved asynchronously and concurrently on different threads. This paper investigates the problem of model checking programs that follow this idiom. We present a programming language SPL that encapsulates this design pattern. SPL extends simplified form of sequential Java to which we add the capability of making asynchronous method invocations in addition to the standard synchronous method calls and the ability to execute asynchronous methods in threads atomically and concurrently. Our main result shows that the control state reachability problem for finite SPL programs is decidable. Therefore, such multithreaded programs can be model checked using the counterexample guided abstraction-refinement framework. 1

Abstract. Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on R in a natural way, and this in turn gives R the structure of a left module over the left group ring R[SX]. We prove that all ideals of R invariant under the action of SX are finitely generated as R[SX]-modules. The proof involves introducing a certain well-quasi-ordering on monomials and developing a theory of Gröbner bases and reduction in this setting. We also consider the concept of an invariant chain of ideals for finite-dimensional polynomial rings and relate it to the finite generation result mentioned above. Finally, a motivating question from chemistry is presented, with the above framework providing a suitable context in which to study it. 1.

A class of permutations is called closed if 2 implies 2 , where the relation is the natural containment of permutations. Let n be the set of all permutations of 1; 2; : : : ; n belonging to . We investigate the counting functions n 7! j n j of closed classes. Our main result says that if j n j < 2 for at least one n 1, then there is a unique k 1 such that F n;k j n j F n;k n holds for all n 1 with a constant c > 0. Here F n;k are the generalized Fibonacci numbers which grow like powers of the largest positive root of x 1. We characterize also the constant and the polynomial growth of closed permutation classes and give two more results on these.