Constraint satisfaction problems in clausal form

This is the report-version of a mini-series of two articles on the foundations of satisfiability of conjunctive normal forms with non-boolean variables, to appear in Fundamenta Informaticae, 2011. These two parts are here bundled in one report, each part yielding a chapter. Generalised conjunctive normal forms are considered, allowing literals of the form "variable not-equal value". The first part sets the foundations for the theory of autarkies, with emphasise on matching autarkies. Main results concern various polynomial time results in dependency on the deficiency. The second part considers translations to boolean clause-sets and irredundancy as well as minimal unsatisfiability. Main results concern classification of minimally unsatisfiable clause-sets and the relations to the hermitian rank of graphs. Both parts contain also discussions of many open problems.Comment: 91 pages, to appear in Fundamenta Informaticae, 2011, as Constraint satisfaction problems in clausal form I: Autarkies and deficiency, Constraint satisfaction problems in clausal form II: Minimal unsatisfiability and conflict structur

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

Algebraic foundations for qualitative calculi and networks

A qualitative representation $\phi$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^\phi = a^\phi | b^\phi$, as we do for ordinary representations, we only require that $c^\phi\supseteq a^\phi | b^\phi \iff c\geq a ; b$, for each $c$ in the algebra. A constraint network is qualitatively satisfiable if its nodes can be mapped to elements of a qualitative representation, preserving the constraints. If a constraint network is satisfiable then it is clearly qualitatively satisfiable, but the converse can fail. However, for a wide range of relation algebras including the point algebra, the Allen Interval Algebra, RCC8 and many others, a network is satisfiable if and only if it is qualitatively satisfiable. Unlike ordinary composition, the weak composition arising from qualitative representations need not be associative, so we can generalise by considering network satisfaction problems over non-associative algebras. We prove that computationally, qualitative representations have many advantages over ordinary representations: whereas many finite relation algebras have only infinite representations, every finite qualitatively representable algebra has a finite qualitative representation; the representability problem for (the atom structures of) finite non-associative algebras is NP-complete; the network satisfaction problem over a finite qualitatively representable algebra is always in NP; the validity of equations over qualitative representations is co-NP-complete. On the other hand we prove that there is no finite axiomatisation of the class of qualitatively representable algebras.Comment: 22 page

A new model for solution of complex distributed constrained problems

In this paper we describe an original computational model for solving different types of Distributed Constraint Satisfaction Problems (DCSP). The proposed model is called Controller-Agents for Constraints Solving (CACS). This model is intended to be used which is an emerged field from the integration between two paradigms of different nature: Multi-Agent Systems (MAS) and the Constraint Satisfaction Problem paradigm (CSP) where all constraints are treated in central manner as a black-box. This model allows grouping constraints to form a subset that will be treated together as a local problem inside the controller. Using this model allows also handling non-binary constraints easily and directly so that no translating of constraints into binary ones is needed. This paper presents the implementation outlines of a prototype of DCSP solver, its usage methodology and overview of the CACS application for timetabling problems

Coordinated constraint relaxation using a distributed agent protocol

The interactions among agents in a multi-agent system for coordinating a distributed, problem solving task can be complex, as the distinct sub-problems of the individual agents are interdependent. A distributed protocol provides the necessary framework for specifying these interactions. In a model of interactions where the agents' social norms are expressed as the message passing behaviours associated with roles, the dependencies among agents can be specified as constraints. The constraints are associated with roles to be adopted by agents as dictated by the protocol. These constraints are commonly handled using a conventional constraint solving system that only allows two satisfactory states to be achieved - completely satisfied or failed. Agent interactions then become brittle as the occurrence of an over-constrained state can cause the interaction between agents to break prematurely, even though the interacting agents could, in principle, reach an agreement. Assuming that the agents are capable of relaxing their individual constraints to reach a common goal, the main issue addressed by this thesis is how the agents could communicate and coordinate the constraint relaxation process. The interaction mechanism for this is obtained by reinterpreting a technique borrowed from the constraint satisfaction field, deployed and computed at the protocol level.The foundations of this work are the Lightweight Coordination Calculus (LCC) and the distributed partial Constraint Satisfaction Problem (CSP). LCC is a distributed interaction protocol language, based on process calculus, for specifying and executing agents' social norms in a multi-agent system. Distributed partial CSP is an extension of partial CSP, a means for managing the relaxation of distributed, over-constrained, CSPs. The research presented in this thesis concerns how distributed partial CSP technique, used to address over-constrained problems in the constraint satisfaction field, could be adopted and integrated within the LCC to obtain a more flexible means for constraint handling during agent interactions. The approach is evaluated against a set of overconstrained Multi-agent Agreement Problems (MAPs) with different levels of hardness. Not only does this thesis explore a flexible and novel approach for handling constraints during the interactions of heterogeneous and autonomous agents participating in a problem solving task, but it is also grounded in a practical implementation