In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarly easy amendment is available for the real line or for Cantor space and the question of strong completeness for these spaces has remained open, together with the more general question of strong completeness for any dense-in-itself metric space. In this paper, we prove that S4 is strongly complete for any dense-in-itself metric space.

A flow line is a conventional manufacturing system where all jobs must be processed on all machines with the same operation sequence. Line buffers allow nonpermutation flowshop scheduling and job sequences to be changed on different machines. A mixed-integer linear programming model for nonpermutation flowshop scheduling and the buffer requirement along with manufacturing implication is proposed. Ant colony optimization based heuristic is evaluated against Taillard's (1993) well-known flowshop benchmark instances, with 20 to 500 jobs to be processed on 5 to 20 machines (stages). Computation experiments show that the proposed algorithm is incumbent to the state-of-the-art ant colony optimization for flowshop with higher job to machine ratios, using the makespan as the optimization criterion.

Spatial grammars are rule-based, generative systems for the specification of formal languages. Set and shape grammar formulations of spatial grammars enable the definition of spatial design languages and the creation of alternative designs. The original formalism includes labels that provide the possibility to restrict the application of rules or to incorporate additional, nongeometric information in grammar rules. Labels have been used in various ways. This paper investigates the different uses of labels in existing spatial grammars, both paper based and computational, and introduces a new concept of three-dimensional (3-D) labels for spatial grammars. The approach consolidates the different label types in one integrated concept. The main use of 3-D labels is that they can simplify the matching of the left-hand side of rules in parametric grammars. A prototype implementation is used to illustrate the approach through a mechanical engineering example of generating robot arm concepts. This approach more readily enables the use of complex solid geometry in the definition and application of parametric rules. Thus, the flexible generation of complex, meaningful design solutions for mechanical engineering applications can be achieved using parametric spatial grammars combined with 3-D labels.

Shift-reduce parsing has been studied extensively for diverse grammars due to the simplicity and running efficiency. However, in the field of constituency parsing, shift-reduce parsers lag behind state-of-the-art parsers. In this paper we propose a semi-supervised approach for advancing shift-reduce constituency parsing. First, we apply the uptraining approach (Petrov, S. et al. 2010. In Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing (EMNLP), Cambridge, MA, USA, pp. 705–713) to improve part-of-speech taggers to provide better part-of-speech tags to subsequent shift-reduce parsers. Second, we enhance shift-reduce parsing models with novel features that are defined on lexical dependency information. Both stages depend on the use of large-scale unlabeled data. Experimental results show that the approach achieves overall improvements of 1.5 percent and 2.1 percent on English and Chinese data respectively. Moreover, the final parsing accuracies reach 90.9 percent and 82.2 percent respectively, which are comparable with the accuracy of state-of-the-art parsers.

Raussen (2010) gave the trace space, which corresponds to the executions of parallel non-looped, non-branching processes as a prod-simplicial complex derived from a poset. The connected components represent equivalent executions. For looped processes, the state space is a torus and the trace space is a disjoint union of trace spaces of deloopings. In the current paper, we develop the index poset for the trace space of the deloopings from the once delooped case. When just one process is looped, the index poset is generated as words in a regular language. We also construct a corresponding automaton.

Appropriate topology and coefficients have a great impact on their models' performances. This paper proposes an enhanced group method of data handling (GMDH) algorithm using a modified Levenberg–Marquardt (LM) method. In this work, evolutionary algorithm and LM techniques are deployed simultaneously for optimal design of both connectivity configuration and associated coefficients of each candidate solution in the evolving population combination. However, use of singular value decomposition technique with LM is considered as a novel method to overcome the problem of initial guess, which is presented for the first time in this research. In order to illustrate the benefits of the proposed algorithm, it has been applied in a Malaysian manufacturing company for forecasting in inventory control. Moreover, a comparison between the basic GMDH algorithm and the enhanced GMDH algorithm is made, and the results show that the accuracy of the proposed method is considerably high with reasonable reduction in processing time. Therefore, the enhanced GMDH method can be used to replace old techniques in an inventory control system to generate a structure when it is applied to a Kanban setting in the just in time system.

This paper addresses the orientation-singularity analysis and the orientationability evaluation of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semi-symmetrical hexagons. Based on the half-angle transformation, an analytical polynomial of degree 13 that represents the orientation-singularity locus of this special class of parallel manipulators at a given position is derived. Graphical representations of the orientation-singularity locus of this class of manipulators are illustrated with examples to demonstrate the results. Based on the description of the orientation-singularity and nonsingular orientation region of this class of parallel manipulators, a performance index, referred to as orientationability, which describes the orientation capability of this class of manipulators at a given position, is introduced. A discretization algorithm is proposed for computing the orientationability of the special class of parallel manipulators at a given position in the workspace. Moreover, the effects of the design parameters and position parameters on the orientationability are also investigated in detail. Based on the orientationability performance index, another performance index, referred to as practical orientationability, representing the practical orientation capability of the manipulators at a given position, is introduced. In this performance index, singularities, the limitations of active and passive joints and link interferences are all taken into consideration. Furthermore, the practical orientationability of the special class of parallel manipulators studied here is also analyzed over several plane sections of the position-workspace in detail.

The present paper presents a new approach to a leader–follower-based dynamic trajectory planning for multirobot formation. A near-optimal trajectory is generated for each robot in a decentralized manner. The main contributions of the current paper are the proposal of a new objective function that considers both collision avoidance and formation requirement for the trajectory generation, and an analytical solution of trajectory parameters in the trajectory optimization. Simulations and experiments on multirobots are performed to demonstrate the effectiveness of the proposed approach to the multirobot formation in a dynamic environment.

We study Maker/Breaker games on the edges of sparse graphs. Maker and Breaker take turns at claiming previously unclaimed edges of a given graph H. Maker aims to occupy a given target graph G and Breaker tries to prevent Maker from achieving his goal. We show that for every d there is a constant c = c(d) with the property that for every graph G on n vertices of maximum degree d there is a graph H on at most cn edges such that Maker has a strategy to occupy a copy of G in the game on H.

This is a result about a game-theoretic variant of the size Ramsey number. For a given graph G, $\hat{r}'(G)$ is defined as the smallest number M for which there exists a graph H with M edges such that Maker has a strategy to occupy a copy of G in the game on H. In this language, our result yields that for every connected graph G of constant maximum degree, $\hat{r}'(G) = \Theta(n)$.

Moreover, we can also use our method to settle the corresponding extremal number for universal graphs: for a constant d and for the class ${\cal G}_{n}$ of n-vertex graphs of maximum degree d, $s({\cal G}_{n})$ denotes the minimum number such that there exists a graph H with M edges where, for everyG ∈ ${\cal G}_{n}$, Maker has a strategy to build a copy of G in the game on H. We obtain that $s({\cal G}_{n}) = \Theta(n^{2 - \frac{2}{d}})$.

We introduce a novel probabilistic algorithm (CPRM) for real-time motion planning in the configuration space ${\EuScript C}$. Our algorithm differs from a probabilistic road map (PRM) algorithm in the motion between a pair of anchoring points (local planner) which takes place on the boundary of the obstacle subspace ${\EuScript O}$. We define a varying potential field f on ∂${\EuScript O}$ as a Morse function and follow $\vec{\nabla} f$. We then exemplify our algorithm on a redundant worm climbing robot with n degrees of freedom and compare our algorithm running results with those of the PRM.

We developed a novel small rat-like robot called Waseda Rat No. 4 (WR-4) to interact with real rats. WR-4 can perform both rearing (rising up on its hind limbs) and rotating (body bending during movement) actions faster than live mature rats. After robot–rat interaction involving rearing and body grooming (body cuddling and head curling) actions of WR-4, real rats showed more activity and greater interest in the robot. Similar results evident from rat–rat interaction suggest that a rat-like robot is able to interact with rats in the same way as real rats. Furthermore, lower variances between the rat subjects in robot–rat interaction reveals that a rat-like robot can more effectively impact rat's behavior in a controllable, predictable way.

Given a set $A\subset\mathbb{Z}_{N}$, we say that a function $f\colon A \to \mathbb{Z}_{N}$ is a Freiman homomorphism if f(a)+f(b)=f(c)+f(d) whenever a,b,c,d ∈ A satisfy a+b=c+d. This notion was introduced by Freiman in the 1970s, and plays an important role in the field of additive combinatorics. We say that A is linear if the only Freiman homomorphisms are functions of the form f(x) = ax+b.

Suppose the elements of A are chosen independently at random, each with probability p. We shall look at the following question: For which values of p=p(N) is A linear with high probability as N → ∞? We show that if p=(2logN − ω(N))1/3N−2/3, where ω(N) → ∞ as N → ∞, then A is not linear with high probability, whereas if p=N−1/2+ε for any ε>0 then A is linear with high probability.

This work studies the typical behaviour of random integer-valued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: M-Lipschitz functions (functions which change by at most M along edges) and integer-homomorphisms (functions which change by exactly 1 along edges). We prove that such functions typically exhibit very small fluctuations. For instance, we show that a uniformly chosen M-Lipschitz function takes only M+1 values on most of the graph, with a double exponential decay for the probability of taking other values.