Complete inference systems for weak bisimulation equivalences in the π-calculus

Proof systems for weak bisimulation equivalences in the π-calculus are presented, and their soundness and completeness are shown. Two versions of π-calculus are investigated, one without and the other with the mismatch operator. For each version of the calculus proof systems for both late and early weak bisimulation equivalences are studied. Thus there are four proof systems in all. These inference systems are related in a natural way: the inference system for early equivalence is obtained from the one for late equivalence by replacing the inference rule for input prefix, while the inference system for the version of π-calculus with mismatch is obtained by adding a single inference rule for mismatch to the one for the version without it. The proofs of the completeness results rely on the notion of symbolic bisimulation.     

A human-computer interactive design program for a multisolution nonlinear problem

An idea of using a human-computer interactive program for an engineering design dealing with a nonlinear multisolution problem is introduced. The example shown is a program for a design of a drainage open channel. The hydraulics and geometry equations for triangular or trapezoidal ditches are to be satisfied by the ditch parameters, which are the side slopes (S_L and S_R), the depth (d) and the width of the bottom (W_b). The data are the flow rate (Q) and maximum allowable flow velocity. After W_b and one of the slopes for a nonsymmetrical ditch (S_L) are chosen by the designer, the other slope and d may be found as a solution of two nonlinear algebraic equations. Instead of trying to solve these equations, the program displays the two curves in s-d coordinate system. If the curves intersect, the designer types in the coordinates of the point of intersection. Otherwise, new curves for decreased velocity are displayed as the indicated key is pressed. The procedure may be continued until the curves intersect. The final parameters chosen by the designer are checked by the program to verify that the actual flow rate and velocity are within the required limits.     

Exponential space complexity for OBDD-based reachability analysis

Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Nevertheless, many basic graph problems are known to be PSPACE-hard if their input graphs are represented by OBDDs. Computing the set of nodes that are reachable from some source s∈V in a digraph G=(V,E) is an important problem in computer-aided design, hardware verification, and model checking. Until now only exponential lower bounds on the space complexity of a restricted class of OBDD-based algorithms for the reachability problem have been known. Here, the result is extended by presenting an exponential lower bound for the general reachability problem. As a by-product a general exponential lower bound is obtained for the computation of OBDDs representing all connected node pairs in a graph, the transitive closure.     

Calculi for interaction

Action structures have previously been proposed as an algebra for both the syntax and the semantics of interactive computation. Here, a class of concrete action structures calledaction calculi is identified, which can serve as a non-linear syntax for a wide variety of models of interactive behaviour. Each action in an action calculus is represented as an assembly ofmolecules; the syntactic binding ofnames is the means by which molecules are bound together. A graphical form,action graphs, is used to aid presentation. One action calculus differs from another only in its generators, calledcontrols. Action calculi generalise a previously defined action structure PIC for the π- calculus. Several extensions to PIC are given as action calculi, giving essentially the same power as the π-calculus. An action calculus is also given for the typed λ-calculus, and for Petri nets parametrized on their places and transitions. An equational characterization of action calculi is given: each action calculusA is the quotient of a term algebra by certain equations. The terms are generated by a set of operators, including those basic to all action structures as well as the controls specific toA; the equations are the basic axioms of action structures together with four additional axiom schemata.     

Bounded query machines: On NP and PSPACE

It is shown that NP is equal to PSPACE if and only if for every oracle set A, NP(A) is equal to the class NPQUERY(A) of languages accepted by nondeterministic polynomial space-bounded oracle machines that are allowed to query the oracle for A only a polynomial number of times. Further, it is shown that there is an oracle set B such that NPQUERY(B) is not equal to the class PQUERY(B) of languages accepted by deterministic polynomial space-bounded oracle machines that are allowed to query the oracle for B only a polynomial number of times.     

Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots

We consider the problem of exploring an anonymous unoriented ring by a team of k identical, oblivious, asynchronous mobile robots that can view the environment but cannot communicate. This weak scenario is standard when the spatial universe in which the robots operate is the two-dimensional plane, but (with one exception) has not been investigated before for networks. Our results imply that, although these weak capabilities of robots render the problem considerably more difficult, ring exploration by a small team of robots is still possible. We first show that, when k and n are not co-prime, the problem is not solvable in general, e.g., if k divides n there are initial placements of the robots for which gathering is impossible. We then prove that the problem is always solvable provided that n and k are co-prime, for k≥17, by giving an exploration algorithm that always terminates, starting from arbitrary initial configurations. Finally, we consider the minimum number ρ(n) of robots that can explore a ring of size n. As a consequence of our positive result we show that ρ(n) is O(logn). We additionally prove that Ω(logn) robots are necessary for infinitely many n.     

Algorithms for regular and irregular coulomb and bessel functions

Algorithms for computing Coulomb-Bessel functions are considered, with emphasis on obtaining accurate values when the argument x is inside the classical turning point x_λ. Algorithms of Barnett et al. for the generalized Coulomb functions and their derivatives are discussed in the context of the phase integral formalism. Modified or alternative algorithms are considered that are designed to be valid for all values of argument x and index λ for the functions F_λ(x), G_λ(x). An algorithm for a ccelerating convergence of a power series by conversion to a continued fraction is presented, and is applied to the evaluation of spherical Bessel functions. An explicit formula for the integrand of the phase integral is presented for spherical Bessel functions. The methods considered need to be augmented by an efficient algorithm for computing the logarithmic derivative of G₀ + iF₀ for Coulomb functions when x is smaller than the charge parameter η.     

Concurrent search for distributed CSPs

A distributed concurrent search algorithm for distributed constraint satisfaction problems (DisCSPs) is presented. Concurrent search algorithms are composed of multiple search processes (SPs) that operate concurrently and scan non-intersecting parts of the global search space. Each SP is represented by a unique data structure, containing a current partial assignment (CPA), that is circulated among the different agents. Search processes are generated dynamically, started by the initializing agent, and by any number of agents during search.In the proposed, ConcDB, algorithm, all search processes perform dynamic backtracking. As a consequence of backjumping, a search space can be found unsolvable by a different search process. This enhances the efficiency of the ConcDB algorithm. Concurrent Dynamic Backtracking is an asynchronous distributed algorithm and is shown to be faster than former algorithms for solving DisCSPs. Experimental evaluation of ConcDB, on randomly generated DisCSPs demonstrates that the network load of ConcDB is similar to the network load of synchronous backtracking and is much lower than that of asynchronous backtracking. The advantage of Concurrent Search is more pronounced in the presence of imperfect communication, when messages are randomly delayed.     

Characterization of growing lettuce from density contours—II. Statistics

The density profiles of standing iceberg lettuce are obtained by recording the transmitted X-ray signal during traverse of the row. From the profile of each single head, five parameters are extracted which are used in a regression analysis to predict weight, W, volume, V, and density, D, of the head when stripped for market display. The regression equations are only slightly dependent on variety for 3 varieties tested (Salinas, Monterey, and Great Lakes) and cover a time span of 17 days, from head formation to one week after optimum maturity. Ninety-two, 81 and 80%, of the variation of W, V, and D, respectively, is accounted for by the regression. The distribution of both independent and dependent variables is found to be consistent with a normal distribution. This is one in a series of papers using X-ray scanners to characterize standing row crops.     

A scalable framework for mobile real-time group communication services

A scalable framework for mobile real-time group communication services is developed in this paper. Examples for possible applications of this framework are mobile social networks, mobile conference calls, mobile instant messaging services, and mobile multi-player on-line games. A key requirement for enabling a real-time group communication service is the tight constraint imposed on the call delivery delay. Since establishing such communication service for a group of independent mobile users under a tight delay constraint is NP-hard, a two-tier architecture is proposed, that can meet the delay constraint imposed by the real-time service requirement for many independent mobile clients in a scalable manner. This goal is achieved by two dimensional partition of the space, first by organization and then geographically. Both the time and memory complexity associated with the location management of N mobile users are O(N) for the location management provided by the proposed framework, while a distributed scheme requires O(N²) for both time and memory complexity.     

Textural approach to generalized rough sets based on relations

This paper presents a discussion on rough set theory from the textural point of view. A texturing is a family of subsets of a given universal set U satisfying certain conditions which are generally basic properties of the power set. The suitable morphisms between texture spaces are given by direlations defined as pairs (r,R) where r is a relation and R is a corelation. It is observed that the presections are natural generalizations for rough sets; more precisely, if (r,R) is a complemented direlation, then the inverse of the relation r (the corelation R) is actually a lower approximation operator (an upper approximation operator).     

On the coordinator's rule for Fast Paxos

Fast Paxos is an algorithm for consensus that works by a succession of rounds, where each round tries to decide a value v that is consistent with all past rounds. Rounds are started by a coordinator process and consistency is guaranteed by the rule used by this process for the selection of v and by the properties of process sets called quorums. We show a simplified version of this rule for the specific case where the quorums are defined by the cardinality of these process sets. This rule is of special interest for implementors of the algorithm.     

Testing equality of covariance matrices when data are incomplete

In the statistics literature, a number of procedures have been proposed for testing equality of several groups’ covariance matrices when data are complete, but this problem has not been considered for incomplete data in a general setting. This paper proposes statistical tests for equality of covariance matrices when data are missing. A Wald test (denoted by T₁), a likelihood ratio test (LRT) (denoted by R), based on the assumption of normal populations are developed. It is well-known that for the complete data case the classic LRT and the Wald test constructed under the normality assumption perform poorly in instances when data are not from multivariate normal distributions. As expected, this is also the case for the incomplete data case and therefore has led us to construct a robust Wald test (denoted by T₂) that performs well for both normal and non-normal data. A re-scaled LRT (denoted by R^*) is also proposed. A simulation study is carried out to assess the performance of T₁, T₂, R, and R^* in terms of closeness of their observed significance level to the nominal significance level as well as the power of these tests. It is found that T₂ performs very well for both normal and non-normal data in both small and large samples. In addition to its usual applications, we have discussed the application of the proposed tests in testing whether a set of data are missing completely at random (MCAR).     

Concurrent checkpoint initiation and recovery algorithms on asynchronous ring networks

Checkpointing with rollback recovery is a well-known method for achieving fault-tolerance in distributed systems. In this work, we introduce algorithms for checkpointing and rollback recovery on asynchronous unidirectional and bi-directional ring networks. The proposed checkpointing algorithms can handle multiple concurrent initiations by different processes. While taking checkpoints, processes do not have to take into consideration any application message dependency. The synchronization is achieved by passing control messages among the processes. Application messages are acknowledged. Each process maintains a list of unacknowledged messages. Here we use a logical checkpoint, which is a standard checkpoint (i.e., snapshot of the process) plus a list of messages that have been sent by this process but are unacknowledged at the time of taking the checkpoint. The worst case message complexity of the proposed checkpointing algorithm is O(kn) when k initiators initiate concurrently. The time complexity is O(n). For the recovery algorithm, time and message complexities are both O(n).     

Generalized fuzzy rough sets determined by a triangular norm

The theory of rough sets has become well established as an approach for uncertainty management in a wide variety of applications. Various fuzzy generalizations of rough approximations have been made over the years. This paper presents a general framework for the study of T-fuzzy rough approximation operators in which both the constructive and axiomatic approaches are used. By using a pair of dual triangular norms in the constructive approach, some definitions of the upper and lower approximation operators of fuzzy sets are proposed and analyzed by means of arbitrary fuzzy relations. The connections between special fuzzy relations and the T-upper and T-lower approximation operators of fuzzy sets are also examined. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, T-fuzzy approximation operators are defined by axioms. Different axiom sets of T-upper and T-lower fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations producing the same operators. The independence of axioms characterizing the T-fuzzy rough approximation operators is examined. Then the minimal sets of axioms for the characterization of the T-fuzzy approximation operators are presented. Based on information theory, the entropy of the generalized fuzzy approximation space, which is similar to Shannon’s entropy, is formulated. To measure uncertainty in T-generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T = min, it is proved that the measure of fuzziness of the generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.     

On LL-regular grammars

Several results pertaining to LL-regular grammars are presented. The decidability of whether or not a grammar is LL-regular for a particular regular partition, which was first stated by Nijholt, and the undecidability of whether or not a regular partition exists for which a grammar is LL-regular are proved. An algorithm for converting an LL-regular grammar into a strong LL-regular grammar that generates the same language is presented, and the construction of a two pass parser is described.     

MGRS: A multi-granulation rough set

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak’s rough set theory are special instances of those of MGRS.Moreover, several important measures, such as accuracy measureα, quality of approximationγ and precision of approximationπ, are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski-Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (“AND” rules) from Pawlak’s rough set model, the form of decision rules in MGRS is “OR”. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations.     

A direct interval extension of TOPSIS method

The TOPSIS method is a technique for order preference by similarity to ideal solution. This technique currently is one of the most popular methods for Multiple Criteria Decision Making (MCDM). The TOPSIS method was primary developed for dealing with only real-valued data. In many cases, it is hard to present precisely the exact ratings of alternatives with respect to local criteria and as a result these ratings are considered as intervals. There are some papers devoted to the interval extensions of TOPSIS method, but these extensions are based on different heuristic approaches to definition of positive and negative ideal solutions. These ideal solutions are presented by real values or intervals, which are not attainable in a decision matrix. Since this is in contradiction with basics of classical TOPSIS method, in this paper we propose a new direct approach to interval extension of TOPSIS method which is free of heuristic assumptions and limitations of known methods. Using numerical examples we show that “direct interval extension of TOPSIS method” may provide the final ranking of alternatives which is substantially different from the results obtained using known methods.     

On the collective sort problem for distributed tuple spaces

In systems coordinated with a distributed set of tuple spaces, it is crucial to assist agents in retrieving the tuples they are interested in. This can be achieved by sorting techniques that group similar tuples together in the same tuple space, so that the position of a tuple can be inferred by similarity. Accordingly, we formulate the collective sort problem for distributed tuple spaces, where a set of agents is in charge of moving tuples up to a complete sort has been reached, namely, each of the N tuple spaces aggregate tuples belonging to one of the N kinds available. After pointing out the requirements for effectively tackling this problem, we propose a self-organizing solution resembling brood sorting performed by ants. This is based on simple agents that perform partial observations and accordingly take decisions on tuple movement. Convergence is addressed by a fully adaptive method for simulated annealing, based on noise tuples inserted and removed by agents on a need basis so as to avoid sub-optimal sorting. Emergence of sorting properties and scalability are evaluated through stochastic simulations.