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1.
An instance of the maximum constraint satisfaction problem (Max CSP) is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Maxk-SAT and Max Cut) and is consequently NP-hard. Thus, it is natural to study how restrictions on the allowed constraint types (or constraint language) affect the complexity and approximability of Max CSP. The PCP theorem is equivalent to the existence of a constraint language for which Max CSP has a hard gap at location 1; i.e. it is NP-hard to distinguish between satisfiable instances and instances where at most some constant fraction of the constraints are satisfiable. All constraint languages, for which the CSP problem (i.e., the problem of deciding whether all constraints can be satisfied) is currently known to be NP-hard, have a certain algebraic property. We prove that any constraint language with this algebraic property makes Max CSP have a hard gap at location 1 which, in particular, implies that such problems cannot have a PTAS unless P=NP. We then apply this result to Max CSP restricted to a single constraint type; this class of problems contains, for instance, Max Cut and Max DiCut. Assuming PNP, we show that such problems do not admit PTAS except in some trivial cases. Our results hold even if the number of occurrences of each variable is bounded by a constant. Finally, we give some applications of our results.  相似文献   

2.
Klaim is an experimental language designed for modeling and programming distributed systems composed of mobile components where distribution awareness and dynamic system architecture configuration are key issues. StocKlaim [R. De Nicola, D. Latella, and M. Massink. Formal modeling and quantitative analysis of KLAIM-based mobile systems. In ACM Symposium on Applied Computing (SAC). ACM Press, 2005. Also available as Technical Report 2004-TR-25; CNR/ISTI, 2004] is a Markovian extension of the core subset of Klaim which includes process distribution, process mobility, asynchronous communication, and site creation. In this paper, MoSL, a temporal logic for StocKlaim is proposed which addresses and integrates the issues of distribution awareness and mobility and those concerning stochastic behaviour of systems. The satisfiability relation is formally defined over labelled Markov chains. A large fragment of the proposed logic can be translated to action-based CSL for which efficient model-checkers exist. This way, such model-checkers can be used for the verification of StocKlaim models against MoSL properties. An example application is provided in the present paper.  相似文献   

3.
The NYU Tvoc project applies the method of translation validation to verify that optimized code is semantically equivalent to the unoptimized code, by establishing, for each run of the optimizing compiler, a set of verification conditions (VCs) whose validity implies the correctness of the optimized run. The core of Tvoc is Tvoc-sp, that handles structure preserving optimizations, i.e., optimizations that do not alter the inner loop structures. The underlying proof rule, Val, on whose soundness Tvoc-sp is based, requires, among other things, to generating invariants at each “cutpoint” of the control graph of both source and target codes. The current implementation of Tvoc-sp employs somewhat naïve fix-point computations to obtain the invariants. In this paper, we propose an alternative method to compute invartiants which is based on simple data-flow analysis techniques.  相似文献   

4.
We present two enhancements of the functional language which is used in the eriFun system to write programs and formulate statements about them. Context dependent procedures allow to stipulate the context under which procedures are sensibly executed, thus avoiding runtime tests in program code as well as verification of absence of exceptions by proving stuck-freeness of procedure calls. Computed types lead to more compact code, increase the readability of programs, and make the well-known benefits of type systems available to non-freely generated data types as well. Since satisfaction of context requirements as well as type checking becomes undecidable, proof obligations are synthesized to be proved by the verifier at hand, thus supporting static code analysis. Information about the type hierarchy is utilized for increasing the performance and efficiency of the verifier.  相似文献   

5.
The programming language synERJY is presented. It integrates object-orientation and synchronous formalisms in the spirit of Esterel, Lustre, and Statecharts.  相似文献   

6.
The Mono Model Checker (mmc) is a software model checker for cil bytecode programs. mmc has been developed on the Mono platform. mmc is able to detect deadlocks and assertion violations in cil programs. The design of mmc is inspired by the Java PathFinder (jpf), a model checker for Java programs. The performance of mmc is comparable to jpf. This paper introduces mmc and presents its main architectural characteristics.  相似文献   

7.
The Improved Primal Simplex (IPS) algorithm [Elhallaoui I, Metrane A, Desaulniers G, Soumis F. An Improved Primal Simplex algorithm for degenerate linear programs. SIAM Journal of Optimization, submitted for publication] is a dynamic constraint reduction method particularly effective on degenerate linear programs. It is able to achieve a reduction in CPU time of over a factor of three on some problems compared to the commercial implementation of the simplex method CPLEX. We present a number of further improvements and effective parameter choices for IPS. On certain types of degenerate problems, our improvements yield CPU times lower than those of CPLEX by a factor of 12.  相似文献   

8.
The goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques. This problem is NP-complete but recently, several parameterized algorithms have been proposed. In this paper, we present a number of surprisingly simple search tree algorithms for Weighted Cluster Editing assuming that edge insertion and deletion costs are positive integers. We show that the smallest search tree has size O(1.82k) for edit cost k, resulting in the currently fastest parameterized algorithm, both for this problem and its unweighted counterpart. We have implemented and compared our algorithms, and achieved promising results.1  相似文献   

9.
The specification language Csp-Casl allows one to model processes as well as data of distributed systems within one framework. In our paper, we describe how a combination of the existing tools Hets and Csp-Prover can solve the challenges that Csp-Casl raises on integrated theorem proving for processes and data. For building this new tool, the automated generation of theorems and their proofs in Isabelle/HOL plays a fundamental role. A case study of industrial strength demonstrates that our approach scales up to complex problems.  相似文献   

10.
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