We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemelä and Simons, uses weight constraints. We show that there is a simple, modular translation from the language of weight constraints into the language of nested expressions that preserves the program's answer sets. Nested expressions can be eliminated from the result of this translation in favor of additional atoms. The translation makes it possible to compute answer sets for some programs with weight constraints using satisfiability solvers, and to prove the strong equivalence of programs with weight constraints using the logic of here-and-there.

We present the Zen toolkit for morphological and phonological processing of natural languages. This toolkit is presented in literate programming style, in the Pidgin ML subset of the Objective Caml functional programming language. This toolkit is based on a systematic representation of finite state automata and transducers as decorated lexical trees. All operations on the state space data structures use the zipper technology, and a uniform sharing functor permits systematic maximum sharing as dags. A particular case of lexical maps is specially convenient for building invertible morphological operations such as inflected forms dictionaries, using a notion of differential word. As a particular application, we describe a general method for tagging a natural language text given as a phoneme stream by analysing possible euphonic liaisons between words belonging to a lexicon of inflected forms. The method uses the toolkit methodology by constructing a non-deterministic transducer, implementing rational rewrite rules, by mechanical decoration of a trie representation of the lexicon index. The algorithm is linear in the size of the lexicon. A coroutine interpreter is given, and its correctness and completeness are formally proved. An application to the segmentation of Sanskrit by sandhi analysis is demonstrated.

We consider a propositional spatial logic for finite trees. The logic includes $\A \Par \B$ (tree composition), $\A \,{\Guarantee}\, \B$ (the implication induced by composition), and $\Zero$ (the unit of composition). We show that the satisfaction and validity problems are equivalent, and decidable. The crux of the argument is devising a finite enumeration of trees to consider when deciding whether a spatial implication is satisfied. We introduce a sequent calculus for the logic, and show it to be sound and complete with respect to an interpretation in terms of satisfaction. Finally, we describe a complete proof procedure for the sequent calculus. We envisage applications in the area of logic-based type systems for semistructured data. We describe a small programming language based on this idea.

This is a tutorial on using type-indexed embedding/projection pairs when writing interpreters in statically-typed functional languages. The method allows (higher-order) values in the interpreting language to be embedded in the interpreted language and values from the interpreted language may be projected back into the interpreting one. This is particularly useful when adding command-line interfaces or scripting languages to applications written in functional languages. We first describe the basic idea and show how it may be extended to languages with recursive types and applied to elementary meta-programming. We then show how the method combines with Filinski's continuation-based monadic reflection operations to define an [lsquor]extensional[rsquor] version of the call-by-value monadic translation and hence to allow values to be mapped bidirectionally between the levels of an interpreter for a functional language parameterized by an arbitrary monad. Finally, we show how SML functions may be embedded into, and projected from, an interpreter for an asynchronous $\pi$-calculus via an ‘extensional’ variant of a standard translation from $\lambda$ into $\pi$.

A decomposition of a set X of words over a d-letter alphabetA = {a1,...,ad} is any sequence X1,...,Xd,Y1,...,Yd of subsets of A* such that the sets X i , i = 1,...,d, are pairwise disjoint,their union is X, and for all i, 1 ≤ i ≤ d, Xi ~ aiYi , where ~denotes the commutative equivalence relation. We introduce some suitable decompositionsthat we call good, admissible, and normal. A normal decomposition is admissible andan admissible decomposition is good. We prove that a set is commutativelyprefix if and only if it has a normal decomposition. In particular, we consider decompositions of Bernoulli sets and codes. We prove that there exist Bernoulli setswhich have no good decomposition. Moreover, we show that the classical conjecture ofcommutative equivalence of finite maximal codes to prefix ones is equivalent to the statementthat any finite and maximal code has an admissible decomposition.

Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandtsemigroup B 2, under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level 3/2 of Straubing-Thérien's concatenation hierarchy has infinite vertex rank.

Consider the random Dirichlet partition of the interval into n fragments at temperature θ > 0. Explicit results on the law of its size-biased permutation are first supplied. Using these, new results on the comparative search cost distributions from Dirichlet partition and from its size-biased permutation are obtained.

Consider a single-commodity inventory system in which the demand is modeled by a sequence of independent and identically distributed random variables that can take negative values. Such problems have been studied in the literature under the name cash management and relate to the variations of the on-hand cash balances of financial institutions. The possibility of a negative demand also models product returns in inventory systems. This article studies a model in which, in addition to standard ordering and scrapping decisions seen in the cash management models, the decision-maker can borrow and store some inventory for one period of time. For problems with back orders, zero setup costs, and linear ordering, scrapping, borrowing, and storage costs, we show that an optimal policy has a simple four-threshold structure. These thresholds, in a nondecreasing order, are order-up-to, borrow-up-to, store-down-to, and scrap-down-to levels; that is, if the inventory position is too low, an optimal policy is to order up to a certain level and then borrow up to a higher level. Analogously, if the inventory position is too high, the optimal decision is to reduce the inventory to a certain point, after which one should store some of the inventory down to a lower threshold. This structure holds for the finite and infinite horizon discounted expected cost criteria and for the average cost per unit time criterion. We also provide sufficient conditions when the borrowing and storage options should not be used. In order to prove our results for average costs per unit time, we establish sufficient conditions when the optimality equations hold for a Markov decision process with an uncountable state space, noncompact action sets, and unbounded costs.

The recently announced Strong Perfect Graph Theorem states that the class ofperfect graphs coincides with the class of graphs containing no inducedodd cycle of length at least 5 or the complement of such a cycle. Agraph in this second class is called Berge. A bull is a graph with fivevertices x, a, b, c, d and five edges xa, xb, ab, ad, bc. A graph isbull-reducible if no vertex is in two bulls. In this paper we give asimple proof that every bull-reducible Berge graph is perfect. Althoughthis result follows directly from the Strong Perfect Graph Theorem, our proofleads to a recognition algorithm for this new class of perfect graphs whosecomplexity, O(n6), is much lower than that announced for perfect graphs.

We show that semigroups representable by triangular matrices over a fixed finite fieldform a decidable pseudovariety and provide a finite pseudoidentity basis for it.

Cover automata for finite languages have been much studied a few years ago.It turns out that a simple mathematical structure, namelysimilarity relations over a finite set of words, is underlying thesestudies. In the present work, we investigate in detail for themselvesthe properties of these relations beyond the scope of finite languages.New results with straightforward proofsare obtained in this generalized framework,and previous results concerning coverautomata are obtained as immediate consequences.

Let P be a hereditary property of words, i.e., aninfinite class of finite words such that every subword (block) ofa word belonging to P is also in P.Extending the classical Morse-Hedlund theorem, we show thateither P contains at least n+1 words of lengthn for every n or, for some N, it contains at most N words of lengthn for every n. More importantly, we prove the following quantitativeextension of this result: if Phas m ≤ n words of length n then, for every k ≥ n + m, it containsat most ⌈(m + 1)/2⌉⌈(m + 1)/2⌈ words of length k.

The problem of controlling transmission rate over a randomly varying channel is cast as a Markov decision process wherein the channel is modeled as a Markov chain. The objective is to minimize a cost that penalizes both buffer occupancy (equivalently, delay) and power. The nature of the optimal policy is characterized using techniques adapted from classical inventory control.

In this paper we investigate how it is possible to recover anautomaton from a rational expression that has been computed from thatautomaton. The notion of derived term of an expression, introduced by Antimirov,appears to be instrumental in this problem. The second important ingredient is the co-minimization of anautomaton, a dual and generalized Moore algorithm on non-deterministicautomata.
We show here that if an automaton is then sufficiently “decorated”, thecombination of these two algorithms gives the desired result. Reducing the amount of “decoration” is still the object of ongoing investigation.

We consider a storage model that can be on or off. When on, the content increases at some state-dependent rate and the system can switch to the off state at a state-dependent rate as well. When off, the content decreases at some state-dependent rate (unless it is at zero) and the system can switch to the on position at a state-dependent rate. This process is a special case of a piecewise deterministic Markov process. We identify the stationary distribution and conditions for its existence and uniqueness.

A subgraph H of a graph G is conformal if G - V(H) has aperfect matching. An orientation D of G is Pfaffian if, forevery conformal even circuit C, the number of edges of C whosedirections in D agree with any prescribed sense of orientation ofC is odd. A graph is Pfaffian if it has a Pfaffianorientation. Not every graph is Pfaffian. However, if G has aPfaffian orientation D, then the determinant of the adjacency matrixof D is the square of the number of perfect matchings of G. (Seethe book by Lovász and Plummer [Matching Theory. Annals of Discrete Mathematics, vol. 9. Elsevier Science (1986), Chap. 8.]A matching covered graph is a nontrivial connected graph inwhich every edge is in some perfect matching. The study of Pfaffianorientations of graphs can be naturally reduced to matching coveredgraphs. The properties of matching covered graphs are thus helpful inunderstanding Pfaffian orientations of graphs. For example, say thattwo orientations of a graph are similar if one can be obtainedfrom the other by reversing the orientations of all the edges in a cutof the graph. Using one of the theorems we proved in [M.H. de Carvalho, C.L. Lucchesi and U.S.R. Murty, Optimal ear decompositions of matching covered graphs. J. Combinat. Theory B85 (2002) 59–93]concerning optimal ear decompositions, we show that if a matchingcovered graph is Pfaffian then the number of dissimilar Pfaffianorientations of G is 2b(G) , where b(G) is the number of“bricks” of G. In particular, any two Pfaffian orientations of abipartite graph are similar. We deduce that the problem ofdetermining whether or not a graph is Pfaffian is as difficult as theproblem of determining whether or not a given orientation is Pfaffian,a result first proved by Vazirani and Yanakakis [Pfaffian orientation of graphs, 0,1 permanents, and even cycles in digraphs.Discrete Appl. Math.25 (1989) 179–180].We establish a simple property of minimal graphs without a Pfaffianorientation and use it to give an alternative proof of thecharacterization of Pfaffian bipartite graphs due to Little [ A characterization of convertible (0,1)-matrices.J. Combinat. Theory B18 (1975) 187–208] .

In this article, we give several results on (multivariate and univariate) stochastic comparisons of generalized order statistics. We give conditions on the underlying distributions and the parameters on which the generalized order statistics are based, to obtain stochastic comparisons in the stochastic, dispersive, hazard rate, and likelihood ratio orders. Our results generalize some recent results for order statistics, record values, and generalized order statistics and provide some new results for other models such as k-record values and order statistics under multivariate imperfect repair.

We study the concept of an H-partition of the vertex set of agraph G, which includes all vertex partitioning problems intofour parts which we require to be nonempty with only externalconstraints according to the structure of a model graph H, withthe exception of two cases, one that has already been classifiedas polynomial, and the other one remains unclassified. In thecontext of more general vertex-partition problems, the problemsaddressed in this paper have these properties: non-list, 4-part,external constraints only (no internal constraints), each partnon-empty. We describe tools that yield for each problemconsidered in this paper a simple and low complexitypolynomial-time algorithm.