Showing papers in "Information & Computation in 2005"

Minimal-change integrity maintenance using tuple deletions

Abstract: We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [in: ACM Symposium on Principles of Database Systems (PODS), 1999, 68] (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable cases. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance.

Comparative branching-time semantics for Markov chains

Abstract: This paper presents various semantics in the branching-time spectrum of discrete-time and continuous-time Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterized in terms of the temporal logics Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL). Apart from presenting various existing branching-time relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and pre-orders in the continuous-and discrete-time setting. The results are summarized in a branching-time spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship.

Tight lower bounds for certain parameterized NP-hard problems

Abstract: Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t-1)-st level W[t-1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted sat, hitting set, set cover, and feature set, cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[1] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weightedq-sat (for any fixed q>=2), clique, independent set, and dominating set, cannot be solved in time n^o^(^k^) unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n^km^O^(^1^) or O(n^k).

Completely iterative algebras and completely iterative monads

Abstract: Completely iterative theories of Calvin Elgot formalize (potentially infinite) computations as solutions of recursive equations. One of the main results of Elgot and his coauthors is that infinite trees form a free completely iterative theory. Their algebraic proof of this result is extremely complicated. We present completely iterative algebras as a new approach to the description of free completely iterative theories. Examples of completely iterative algebras include algebras on complete metric spaces. It is shown that a functor admits an initial completely iterative algebra iff it has a final coalgebra. The monad given by free completely iterative algebras is proved to be the free completely iterative monad on the given endofunctor. This simplifies substantially all previous descriptions of these monads. Moreover, the new approach is much more general than the classical one of Elgot et al. A necessary and sufficient condition for the existence of a free completely iterative monad is proved.

A theory of regular MSC languages

Abstract: Message sequence charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs. A commonly used technique to generate a collection of MSCs is to use a hierarchical message sequence chart (HMSC). We show that the class of languages arising from the so-called bounded HMSCs constitute a proper subclass of the class of regular MSC languages. In fact, we characterize the bounded HMSC languages as the subclass of regular MSC languages that are finitely generated.

Verification of programs with half-duplex communication

Abstract: We consider the analysis of infinite half-duplex systems made of finite state machines that communicate over unbounded channels. The half-duplex property for two machines and two channels (one in each direction) says that each reachable configuration has at most one channel non-empty. We prove in this paper that such half-duplex systems have a recognizable reachability set. We show how to compute, in polynomial time, a symbolic representation of this reachability set and how to use that description to solve several verification problems. Furthermore, though the model of communicating finite state machines is Turing-powerful, we prove that membership of the class of half-duplex systems is decidable. Unfortunately, the natural generalization to systems with more than two machines is Turing-powerful. We also prove that the model-checking of those systems against PLTL (propositional linear temporal logic) or CTL (computational tree logic) is undecidable. Finally, we show how to apply the previous decidability results to the Regular Model Checking. We propose a new symbolic reachability semi-algorithm with accelerations which successfully terminates on half-duplex systems of two machines and some interesting non-half-duplex systems.

A theory of stochastic systems part I: Stochastic automata

Abstract: This paper presents the theoretical underpinning of a model for symbolically representing probabilistic transition systems, an extension of labelled transition systems for the modelling of general (discrete as well as continuous or singular) probability spaces. These transition systems are particularly suited for modelling softly timed systems, real-time systems in which the time constraints are of random nature. For continuous probability spaces these transition systems are infinite by nature. Stochastic automata represent their behaviour in a finite way. This paper presents the model of stochastic automata, their semantics in terms of probabilistic transition systems, and studies several notions of bisimulation. Furthermore, the relationship of stochastic automata to generalised semi-Markov processes is established.

The Seal Calculus

Abstract: The Seal Calculus is a process language for describing mobile computation. Threads and resources are tree structured; the nodes thereof correspond to agents, the units of mobility. The Calculus extends a @p-calculus core with synchronous, objective mobility of agents over channels. This paper systematically compares all previous variants of Seal Calculus. We study their operational behaviour with labelled transition systems and bisimulations; by comparing the resulting algebraic theories we highlight the differences between these apparently similar approaches. This leads us to identify the dialect of Seal that is most amenable to operational reasoning and can form the basis of a distributed programming language. We propose type systems for characterising the communications in which an agent can engage. The type systems thus enforce a discipline of agent mobility, since the latter is coded in terms of higher-order communication.

The existential theory of equations with rational constraints in free groups is PSPACE-complete

Abstract: It is well-known that the existential theory of equations in free groups is decidable. This is a celebrated result of Makanin which was published 1982. Makanin did not discuss complexity issues, but later it was shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in polynomial space. This improvement is based upon an extension of Plandowski's techniques for solving word equations. We present a pspace-algorithm in a more general setting where each variable has a rational constraint, that is, the solution has to respect a specification given by a regular word language. We obtain our main result about the existential theory in free groups as a corollary of the corresponding statement in free monoids with involution.

Particle Swarm Optimization Algorithm

Abstract: This paper introduces and analyzes systematically t he principle, process and parameters of particle swarm optimization (PSO) algori thm, and their influence on optimization performance of PSO Various improved pa rticle swarm optimization algorithms are discussed The algorithm principle and algorithm parameters of multi-phase particle swarm optimization (MPPSO) algorit hm, and their influence on optimization performance of MPPSO are analyzed At la st, applications of PSO algorithm are discussed, and further research issues and some suggestions are given

Some Statistical Analysis of the Normal Cloud Model

Abstract: The probability distributions of the cloud drop and its certainty degree are analyzed. Then the definition of the expectation curve of the normal cloud model is given. Finally, the trends and rules of the normal cloud model, of which the shapes envolve as the parameters change, are discussed. All the above stochastic analysis has some values in theory and application, and will help to develop and perfect the normal cloud model in a wider and higher level.

On the computational power of probabilistic and quantum branching program

Abstract: In this paper, we show that one-qubit polynomial time computations are as powerful as NC^1 circuits. More generally, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show that any NC^1 language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC^1=ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC^1. For read-once quantum branching programs (QBPs), we give a symmetric Boolean function which is computable by a read-once QBP with O(logn) width, but not by a deterministic read-once BP with o(n) width, or by a classical randomized read-once BP with o(n) width which is ''stable'' in the sense that its transitions depend on the value of the queried variable but do not vary from step to step. Finally, we present a general lower bound on the width of read-once QBPs, showing that our O(logn) upper bound for this symmetric function is almost tight.

Notions of bisimulation and congruence formats for SOS with data

Abstract: While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. First, Plotkin's style of Structural Operational Semantics has become a standard in defining operational semantics. Second, congruence with respect to some notion of bisimilarity is an interesting property for such languages and it is essential in reasoning. Third, there are numerous languages that contain an explicit data part in the state of the operational semantics. The first two facts have resulted in a line of research exploring syntactic formats of operational rules to derive the desired congruence property for free. However, the third point (in combination with the first two) is not sufficiently addressed and there is no standard congruence format for operational semantics with an explicit data state. In this article, we address this problem by studying the implications of the presence of a data state on the notion of bisimilarity. Furthermore, we propose a number of formats for congruence.

Verification of probabilistic systems with faulty communication

Abstract: Many protocols are designed to operate correctly even in the case where the underlying communication medium is faulty. To capture the behavior of such protocols, Lossy Channel Systems (LCS's) have been proposed. In an LCS the communication channels are modeled as unbounded FIFO buffers which are unreliable in the sense that they can nondeterministically lose messages. Recently, several attempts have been made to study Probabilistic Lossy Channel Systems (PLCS's) in which the probability of losing messages is taken into account. In this article, we consider a variant of PLCS's which is more realistic than those studied previously. More precisely, we assume that during each step in the execution of the system, each message may be lost with a certain predefined probability. We show that for such systems the following model-checking problem is decidable: to verify whether a linear-time property definable by a finite-state @w-automaton holds with probability one. We also consider other types of faulty behavior, such as corruption and duplication of messages, and insertion of new messages, and show that the decidability results extend to these models.

Secrecy and group creation

Abstract: We add an operation of group creation to the typed @p-calculus, where a group is a type for channels. Creation of fresh groups has the effect of statically preventing certain communications, and can block the accidental or malicious leakage of secrets. Intuitively, no channel belonging to a fresh group can be received by processes outside the initial scope of the group, even if those processes are untyped. We formalize this intuition by adapting a notion of secrecy introduced by Abadi, and proving a preservation of secrecy property.

The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages

Abstract: The growing context-sensitive languages have been classified through the shrinking two-pushdown automaton, the deterministic version of which characterizes the class of generalized Church-Rosser languages [Inform. Comput. 141 (1998) 1]. Exploiting this characterization we prove that the latter class coincides with the class of Church-Rosser languages that was introduced by McNaughton et al. [J. ACM 35 (1988) 324]. Based on this result several open problems of McNaughton et al. are solved. In addition, we show that shrinking two-pushdown automata and length-reducing two-pushdown automata are equivalent, both in the non-deterministic and the deterministic case, thus obtaining still another characterization of the growing context-sensitive languages and the Church-Rosser languages, respectively.

Bridging the gap between fair simulation and trace inclusion

Abstract: The paper considers the problem of checking abstraction between two finite-state fair discrete systems. In automata-theoretic terms this is trace inclusion between two nondeterministic Streett automata. We propose to reduce this problem to an algorithm for checking fair simulation between two generalized Buchi automata. For solving this question we present a new triply nested @m-calculus formula which can be implemented by symbolic methods. We then show that every trace inclusion of this type can be solved by fair simulation, provided we augment the concrete system (the contained automaton) by an appropriate 'non-constraining' automaton. This establishes that fair simulation offers a complete method for checking trace inclusion for finite-state systems. We illustrate the feasibility of the approach by algorithmically checking abstraction between finite state systems whose abstraction could only be verified by deductive methods up to now.

Fast approximate PCPs for multidimensional bin-packing problems

Abstract: We consider approximate PCPs for multidimensional bin-packing problems. In particular, we show how a verifier can be quickly convinced that a set of multidimensional blocks can be packed into a small number of bins. The running time of the verifier is bounded by O(logd n) where n is the number of blocks and d is the dimension.

A theory of Stochastic systems. Part II: Process algebra

Abstract: This paper introduces ♠ (pronounce spades), a stochastic process algebra for discrete-event systems, that extends traditional process algebra with timed actions whose delay is governed by general (a.o. continuous) probability distributions. The operational semantics is defined in terms of stochastic automata, a model that uses clocks--like in timed automata--to symbolically represent randomly timed systems, cf. the accompanying paper [P.R. D'Argenio, J.-P. Katoen, A theory of stochastic systems. Part I: Stochastic automata. Inf. Comput. (2005), to appear]. We show that stochastic automata and ♠ are equally expressive, and prove that the operational semantics of a term up to α-conversion of clocks, is unique (modulo symbolic bisimulation). (Open) probabilistic and structural bisimulation are proven to be congruences for ♠, and are equipped with an equational theory. The equational theory is shown to be complete for structural bisimulation and allows to derive an expansion law.

Communication and mobility control in boxed ambients

Abstract: Boxed Ambients (BA) replace Mobile Ambients' open capability with communication primitives acting across ambient boundaries. The expressiveness of the new communication model is achieved at the price of communication interferences whose resolution requires synchronisation of activities at multiple, distributed locations. We study a variant of BA aimed at controlling communication as well as mobility interferences. Our calculus modifies the communication mechanism of BA, and introduces a new form of co-capability, inspired from Safe Ambients (SA) (with passwords), that registers incoming agents with the receiver ambient while at the same time performing access control. We prove that the new calculus has a rich semantics theory, including a sound and complete coinductive characterisation, and an expressive, yet simple type system. Through a set of examples, and an encoding, we characterise its expressiveness with respect to both BA and SA.

Types and full abstraction for polyadic π-calculus

Abstract: A type system for terms of the monadic @p-calculus is introduced and used to obtain a full-abstraction result for the translation of the polyadic @p-calculus into the monadic calculus: well-sorted terms of the polyadic calculus are barbed congruent iff their translations are typed barbed congruent.

The equational theory of regular words

Abstract: Courcelle introduced the study of regular words, i.e., words isomorphic to frontiers of regular trees. Heilbrunner showed that a nonempty word is regular iff it can be generated from the singletons by the operations of concatenation, omega power, omega-op power, and the infinite family of shuffle operations. We prove that the algebra of nonempty regular words on the set A, equipped with these operations, is freely generated by A in a variety which is axiomatizable by an infinite collection of some natural equations. We also show that this variety has no finite equational basis and that its equational theory is decidable in polynomial time.

Competing provers yield improved Karp-Lipton collapse results

Abstract: Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2A = S2. Building on this, we strengthen the Kamper-AFK theorem, namely, we prove that if NP ⊆ (NP ∩ coNP)/poly then the polynomial hierarchy collapses to S2NP∩coNP. We also strengthen Yap's theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to S2NP. Under the same assumptions, the best previously known collapses were to ZPPNP and ZPPNPNP, respectively ([SIAM Journal on Computing 28 (1) (1998) 311; Journal of Computer and System Sciences 52 (3) (1996) 421], building on [Proceedings of the 12th ACM Symposium on Theory of Computing, ACM Press, New York, 1980, pp. 302-309; Journal of Computer and System Sciences 39 (1989) 21; Theoretical Computer Science 85 (2) (1991) 305; Theoretical Computer Science 26 (3) (1983) 287]). It is known that S2 ⊆ ZPPNP [Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Silver Spring, MD, 2001, pp. 620-629]. That result and its relativized version show that our new collapses indeed improve the previously known results. The Kamper-AFK theorem and Yap's theorem are used in the literature as bridges in a variety of results--ranging from the study of unique solutions to issues of approximation--and so our results implicitly strengthen those results.

An axiomatization of PCTL

Abstract: A sound and complete axiomatization for a computation tree logic with past operators, PCTL*, is given. The logic extends the standard branching time logic CTL* of R-generable models via the use of past time operators and semantics based on a finite linear past leading back from any point in any fullpath. Furthermore, the valid formulas of CTL* are also valid in PCTL*. The past operators allow us to avoid use of any unusual rules of inference such as the ugly automata-motivated AA rule which is part of the existing complete axiomatization for CTL*.

Timer formulas and decidable metric temporal logic

Abstract: We define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate logic. Its canonical model is the real line (and not an @w-sequence of some type). It can be interpreted either by behaviors with finite variability or by unrestricted behaviors. For finite variability models it is as expressive as any logic suggested in the literature. For unrestricted behaviors our treatment is new. In both cases we prove decidability and complexity bounds using general theorems from logic (and not from automata theory). The technical proof uses a sublanguage of the metric monadic logic of order, the language of timer normal form formulas. Metric formulas are reduced to timer normal form and timer normal form formulas allow elimination of the metric.

Reductions between disjoint NP-pairs

Abstract: Disjoint NP-pairs are pairs (A, B) of nonempty, disjoint sets in NP. We prove that all of the following assertions are equivalent: There is a many-one complete disjoint NP-pair; there is a strongly many-one complete disjoint NP-pair; there is a Turing complete disjoint NP-pair such that all reductions are smart reductions; there is a complete disjoint NP-pair for one-to-one, invertible reductions; the class of all disjoint NP-pairs is uniformly enumerable. Let A, B, C, and D be nonempty sets belonging to NP. A smart reduction between the disjoint NP-pairs (A, B) and (C, D) is a Turing reduction with the additional property that if the input belongs to A ∪ B, then all queries belong to C ∪ D. We prove under the reasonable assumption that UP ∩ co-UP has a P-bi-immune set that there exist disjoint NP-pairs (A, B) and (C, D) such that (A, B) is truth-table reducible to (C, D), but there is no smart reduction between them. This paper contains several additional separations of reductions between disjoint NP-pairs. We exhibit an oracle relative to which DistNP has a truth-table-complete disjoint NP-pair, but has no many-one-complete disjoint NP-pair.

Decidable call-by-need computations in term rewriting

Abstract: The theorem of Huet and Levy stating that for orthogonal rewrite systems (i) every reducible term contains a needed redex and (ii) repeated contraction of needed redexes results in a normal form if the term under consideration has a normal form, forms the basis of all results on optimal normalizing strategies for orthogonal rewrite systems. However, needed redexes are not computable in general. In the paper we show how the use of approximations and elementary tree automata techniques allows one to obtain decidable conditions in a simple and elegant way. Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of rewrite systems. We also study modularity aspects of the classes in our hierarchy. It turns out that none of the classes is preserved under signature extension. By imposing various conditions we recover the preservation under signature extension. By imposing some more conditions we are able to strengthen the signature extension results to modularity for disjoint and constructor-sharing combinations.

An efficient query learning algorithm for ordered binary decision diagrams

Abstract: In this paper, we propose a new algorithm that exactly learns ordered binary decision diagrams (OBDDs) with a given variable ordering via equivalence and membership queries. Our algorithm uses at most n equivalence queries and at most 2n(⌈log2m⌉ + 3n) membership queries, where n is the number of nodes in the target-reduced OBDD and m is the number of variables. The upper bound on the number of membership queries is smaller by a factor of O(m) compared with that for the previous best known algorithm proposed by R. Gavalda and D. Guijarro [Learning Ordered Binary Decision Diagrams, Proceedings of the 6th International Workshop on Algorithmic Learning Theory, 1995, pp. 228-238].

Using heuristic search for finding deadlocks in concurrent systems

Abstract: Model checking is a formal technique for proving the correctness of a system with respect to a desired behavior. This is accomplished by checking whether a structure representing the system (typically a labeled transition system) satisfies a temporal logic formula describing the expected behavior. Model checking has a number of advantages over traditional approaches that are based on simulation and testing: it is completely automatic and when the verification fails it returns a counterexample that can be used to pinpoint the source of the error. Nevertheless, model checking techniques often fail because of the state explosion problem: transition systems grow exponentially with the number of components. The aim of this paper is to attack the state explosion problem that may arise when looking for deadlocks in concurrent systems described through the Calculus of Communicating Systems. We propose to use heuristics-based techniques, namely the A* algorithm, both to guide the search without constructing the complete transition system, and to provide minimal counterexamples. We have realized a prototype tool to evaluate the methodology. Experiments we have conducted on processes of different size show the benefit from using our technique against building the whole state space, or applying some other methods.

Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data

Abstract: In this paper, we consider an ordinal on-line scheduling problem. A sequence of n independent jobs has to be assigned non-preemptively to two uniformly related machines. We study two objectives which are maximizing the minimum machine completion time, and minimizing the lp, norm of the completion times. It is assumed that the values of the processing times of jobs are unknown at the time of assignment. However it is known in advance that the processing times of arriving jobs are sorted in a non-increasing order. We are asked to construct an assignment of all jobs to the machines at time zero, by utilizing only ordinal data rather than actual magnitudes of jobs. For the problem of maximizing the minimum completion time we first present a comprehensive lower bound on the competitive ratio, which is a piecewise function of machine speed ratio s. Then, we propose an algorithm which is optimal for any s ≥ 1. For minimizing the lp norm, we study the case of identical machines (s = 1) and present tight bounds as a function of p.