A Systematic Framework for Solving Geometric Constraints Analytically

Optimization and relaxation are two important operations that naturally arise in many applications involving constraints, e.g., engineering design, scheduling, decision support, etc. In optimization, we are interested in finding the optimal (i.e., best) solutions to a set of constraints with respect to an objective function. In many applications, optimal solutions may be difficult or impossible to obtain, and hence we are interested in finding suboptimal solutions, by either relaxing the constraints or relaxing the objective function. The contribution of this paper lies in providing a logical framework for performing optimization and relaxation in a constraint logic programming language. Our proposed framework is called preference logic programming (PLP), and its use for optimization was discussed in [8]. Essentially, in PLP we can designate certain predicates as optimization predicates, and we can specify the objective function by stating preference criteria for determining the optimal solutions to these predicates. This paper extends the PLP paradigm with facilities to formulate relaxation problems in a natural manner. We introduce the concept of a relaxation goal, and discuss its use for preference relaxation. Our model-theoretic semantics of relaxation is based on simple concepts from modal logic: Essentially, each world in the possible-worlds semantics for a preference logic program is a model for the constraints of the program, and an ordering over these worlds is determined by the objective function. Optimization can then be expressed as truth in strongly optimal worlds, while relaxation becomes truth in suitably-defined suboptimal worlds. We also present an operational semantics for relaxation as well as correctness results. Our conclusion is that the concept of preference provides a unifying framework for formulating optimization as well as relaxation problems.

Optimization and relaxation in constraint logic languages

The complexity of designs continues to rise, driven by technology advances, while time-tomarket imposes always shorter time. Moreover, the increasing of design complexity implies that design verification becomes one of the most cost-dominating phase in design production. Functional Automatic Test Pattern Generators (ATPGs) based on simulation (Corno et al., 2001; Fin & Fummi, 2003a) are fast, but generally, they are unable to cover corner cases, and they cannot prove untestability. On the contrary, functional ATPGs exploiting formal methods (Ghosh & Fujita, 2001; Zhang et al., 2003; Xin et al., 2005a), are exhaustive and cover corner cases, but they tend to suffer of the state explosion problem when adopted for verifying large designs. In this context, a functional ATPG is presented, that relies on the joint use of pseudo-deterministic simulation and constraint logic programming (CLP) (Jaffar & Maher, 1994), to generate high-quality test sequences for solving complex problems. Thus, the advantages of both simulation-based and static-based verification techniques are preserved, while their respective drawbacks are limited. In particular, CLP, a form of constraint programming in which logic programming is extended to include concepts from constraint satisfaction, is well-suited to be jointly used with simulation. In fact, information learned during design exploration by simulation can be effectively exploited for guiding the search of a CLP solver towards design under verification (DUV) areas not covered yet. Therefore, this work is focused on the use of CLP for addressing corner cases during functional test pattern generation. In particular, a CLP-based fault-oriented ATPG engine is proposed to be adopted, after simulation, learning and random-walk/backjumping, as the last step of the incremental test generation flow showed in Figure 1. According to such a flow, the ATPG framework is composed of three functional ATPG engines working on three different models of the same DUV: the hardware description language (HDL) model of the DUV, the set of concurrent EFSMs extracted from the HDL description, and the set of logic constraints modelling the EFSMs. The EFSM paradigm has been selected since it allows a compact representation of the DUV state space (Lee & Yannakakis, 1992) that limits the state explosion problem typical of more traditional FSMs. In the proposed framework, the first engine is random-based, the second is transitionoriented, while the last is fault-oriented. This approach quickly covers the greater part of DUV faults, typically easy-to-detect faults. Then, the transition-oriented engine and fault-

/pdf/test-generation-based-on-clp-1rypss1jo7.pdf

Test Generation Based on CLP

An interesting exercise for a research community is to foresee its future, identify key research challenges and open problems and be forward-looking in both technology and application fields The Constraint Programming community, in more than 20 years, has performed this exercise several times One example is the recent book on Trends in Constraint Programming edited in 2007 by Benhamou, Jussien and O’Sullivan [1] and the recent challenge paper at AAAI 2012 by O’Sullivan [17] entitled Opportunities and challenges for Constraint Programming Other examples are the earlier papers by Van Hentenryck and Saraswat [8] on Strategic Directions in Constraint Programming in 1996 and the ACM 50th Anniversary Issue of ACM Computing Surveys of the same year on Strategic Directions in Computing Research containing a number of forward looking papers [2–7, 9–16, 18–21] Some of these papers have correctly foreseen the future, some challenges have received less then expected attention, but overall these papers have always provided a useful guide for researchers and newcomers Here we are offering another snapshot of the constraint programming community and what its members consider as promising directions We have intentionally invited contribution without structuring them into a schema Rather we have preferred a bottom-up call for proposals providing supported-by-evidence viewpoints on future directions of CP

/pdf/looking-into-the-crystal-ball-a-bright-future-for-cp-2gl4kxeeyh.pdf

Looking into the crystal-ball: a bright future for CP

We present a theoretical framework, which is based upon notions of ordered hypergraphs and antichain polyhedra, and which is dedicated to the combinatorial analysis of preemptive scheduling problems submitted to parallelization constraints. This framework allows us to characterize specific partially ordered structures which are such that induced preemptive scheduling problems may be solved through linear programming. To prove that, in the general case, optimal preemptive schedules may be searched inside some connected subset of the vertex set of an Antichain Polyhedron.

Preemptive scheduling and antichain polyhedra

We begin by formulating a general framework for constraint programming that we shall use to explain its specific aspects. First, we formulate our initial problem as a CSP. This in itself can be a non-trivial problem. In particular, at this stage we have to take decisions concerning the choice of variables, domains and constraints. As already mentioned in Chapter 1 this phase of constraint programming is called modelling and in contrast to programming in other programming styles it is more time consuming and more involved. Modelling is more an art than science and a number of rules of thumb and various heuristics are useful at this stage. Subsequently, we apply to the formulated CSP the following procedure:

Constraint programming

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Constraint programming