A common type of symmetry is when both variables and values partition into interchangeable sets. Polynomial methods have been introduced to eliminate all symmetric solutions introduced by such interchangeability. Unfortunately, whilst eliminating all symmetric solutions is tractable in this case, pruning all symmetric values is NP-hard. We introduce a new global constraint called SIGLEX and its GAC propagator for pruning some (but not necessarily all) symmetric values. We also investigate how different postings of the SIGLEX constraints affect the pruning performance during constraint solving. Finally, we test these static symmetry breaking constraints experimentally for the first time.

A widely adopted approach to solving constraint satisfaction problems combines systematic tree search with constraint propagation for pruning the search space. Constraint propagation is performed by propagators implementing a certain notion of consistency. Bounds consistency is the method of choice for building propagators for arithmetic constraints and several global constraints in the finite integer domain. However, there has been some confusion in the definition of bounds consistency. In this paper we clarify the differences and similarities among the three commonly used notions of bounds consistency.

Constraint satisfaction is one of the major areas in AI that has important real-life applications. Lee et al. propose E-GENET, a stochastic solver for general constraint solving based on iterative repair. Performance figures show that E-GENET compares favorably against tree-search based solvers in many hard problems. On the other hand, global constraints have been shown to be very effective in modeling complicated CSP's. They have also improved substantially the efficiency of tree-search based solvers in solving real-life problems. In this paper, we present a comprehensive and efficient library of elementary and global constraints for E-GENET. Such a library is essential for applying E-GENET to complex real-life applications. We first present the improved performance of some constraints that appear in our previous papers, followed by the implementation details of three additional global constraints available in the CHIP constraint language. Experimental results, using standard benchmarks and a real-life problem, confirm empirically that the E-GENET architecture is comparable to, if not better than, state of the art in constraint solver technology. IntroductionThe research into constraint satisfaction problems (CSP) [14] is one of the major topics in artificial intelligence that have important real-life applications. A CSP can be stated as follows. We are given a finite set V of variables. Each variable z ranges over its domain D~, a finite set of discrete constants. There is a finite set C of constraints over these variables, which limits the allowed combination of values that can be taken by the variables. The goal is to find a consistent assignment of values to the variables so that all constraints are satisfied. Two main approaches to tackle CSP's are backtracking tree-search, probably enhanced with consistency algorithms [10], and iterative repair methods [15]. An extension of GENET [5], E-GENET [11, 12] is a stochastic solver for general constraint solving based on iterative repair. Performance figures show that E-GENET compares favorably against tree-search based solvers (such as CHIP [7]) * This project is supported in part by a CUHK Direct Grant.

Abstract. "Online Learning" has been commonly viewed as a mechanism for empowering improved learning outcome, increased flexibility of aligning the individual need of learners, and better quality of educational interaction. In fact, a lot of "digitized" and "ready-to-use" learning and teaching resources are already available online; nevertheless, we must not confuse quantity and quality, as these resources may just continue to perpetuate teacher-centred approaches, rather than student-centred approaches. The present research aimed to compare the educational values, learning effectiveness, students and teachers' perceptions of a new online educational paradigm -Situated Game-based Learning with Traditional Web-based Learning in secondary education in Hong Kong. A combination of quantitative and qualitative research methods were employed for data collection and analysis. Results showed that, under the present research settings, although no significant difference of students' learning outcome with respect to these two approaches was found, the participating students and teachers were quite positive towards the educational paradigm of Situated Game-based Learning. This provides vital insights and a basis for further investigating the paradigm's application and development for learning and teaching.

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