In this paper we consider integration of SMT solvers with the filtering algorithms for the finite domain alldifferent constraint. Such integration makes SMT solvers suitable for solving constraint satisfaction problems with the alldifferent constraint involved. First, we present a novel algorithm for explaining inconsistencies and propagations in the alldifferent constraint. We compare it to Katsirelos' algorithm and flow-based algorithms that are commonly used for that purpose. Then we describe our DPLL(T)-compliant SMT theory solver for constraint satisfaction problems that include alldifferent constraints. We also provide an experimental evaluation of our approach.
In order to apply canonical labelling of graphs and isomorphism checking in
interactive theorem provers, these checking algorithms must either be
mechanically verified or their results must be verifiable by independent
checkers. We analyze a state-of-the-art algorithm for canonical labelling of
graphs (described by McKay and Piperno) and formulate it in terms of a formal
proof system. We provide an implementation that can export a proof that the
obtained graph is the canonical form of a given graph. Such proofs are then
verified by our independent checker and can be used to confirm that two given
graphs are not isomorphic.
Abstract. In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.
In order to be able to apply graph isomorphism checking within interactive theorem provers, either graph isomorphism checking algorithms must be mechanically verified, or their results must be verifiable by independent checkers. We analyze a stateof-the-art graph isomorphism checking algorithm (described by McKay and Piperno) and formulate it in a form of a formal proof system. We provide an implementation that can export a proof that an obtained graph is the canonical form of a given graph. Such proofs are then verified by our independent checker, and are used to certify that two given graphs are non-isomorphic.
The transition to a contractual relationship between government and Infrastructure Manager under Directive 2012/34 /EU requires the possession of contract management skills and the development of key performance indicators (KPIs). Previous activities related to the Multi Annual Infrastructure Contract (MAIC) have been exclusively in the field of the Annual Infrastructure Maintenance Program implementation (railway maintenance, public procurement, and supervision of civil works implementation). However, under Directive 2012/34/EU it is necessary to introduce a system of performance indicators for upgrading/modernize infrastructure to obtain value for money. The paper presents a systematic approach in determining the KPIs and their merits on the example of a contract between the Government of Montenegro and the Railway Infrastructure manager of Montenegro (ŽICG JSC) with the aim to improve the operation and quality of services of ŽICG JSC and the condition of railway infrastructure in Montenegro as well. Keywords – Key performance indicators, railway infrastructure Multi-annual contract. Keywords – Key performance indicators, railway infrastructure Multi-annual contract.
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