Sergio Mera

Expressive Power and Decidability for Memory Logics

Taking as inspiration the hybrid logic

The Expressive Power of Memory Logics

\mathcal{HL}({\downarrow})

Algorithms for finding clique-transversals of graphs

, we introduce a new family of logics that we call memory logics. In this article we present in detail two interesting members of this family defining their formal syntax and semantics. We then introduce a proper notion of bisimulation and investigate their expressive power (in comparison with modal and hybrid logics). We will prove that in terms of expressive power, the memory logics we discuss in this paper are more expressive than orthodox modal logic, but less expressive than

Algorithms for clique-independent sets on subclasses of circular-arc graphs

\mathcal{HL}({\downarrow})

Computational Models for Normative Multi-Agent Systems

. We also establish the undecidability of their satisfiability problems.

Tableaux and Model Checking for Memory Logics

We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic HL(↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain. This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic K and HL(↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized.

Completeness Results for Memory Logics

Abstract A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τc of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τc. This algorithm is employed for finding the minimum cardinality clique-transversal of

Clique-independent sets of Helly circular-arc graphs

\overline{3K_{2}}

A Software Tool for Legal Drafting

-free circular-arc graphs in O(n4) time. Further we describe an algorithm for determining τc of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n2) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n2) time.

Completeness results for memory logics

A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a 3K2-free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n2). These algorithms suppose that an HCA model of the graph is given.