Randomisation and Derandomisation in Descriptive Complexity Theory

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures

On the Complexity of Model Expansion

Abstract. We study the complexity of model expansion (MX), which is the prob-lem of expanding a given finite structure with additional relations to produce a finite model of a given formula. This is the logical task underlying many prac-tical constraint languages and systems for representing and solving search prob-lems, and our work is motivated by the need to provide theoretical foundations for these. We present results on both data and combined complexity of MX for several fragments and extensions of FO that are relevant for this purpose, in par-ticular the guarded fragment GFk of FO and extensions of FO and GFk with inductive definitions. We present these in the context of the two closely related, but more studied, problems of model checking and finite satisfiability. To obtain results on FO(ID), the extension of FO with inductive definitions, we provide translations between FO(ID) with FO(LFP), which are of independent interest.

Capturing the Moment. Identity and the Political in Narcís Comadira’s Poems

Narcís Comadira (Girona 1942 – ) started his studies in the monastery of Montserrat in the sixties but abandoned his religious career and became one of the youngest Catalans to join the then newly born Assemblea de Catalunya the activities of which extended over the period 1971-1977, escaping the claustrophobia of Franco’s Spain by going abroad as a Spanish Lector at Queen Mary’s College in London between 1971 and 1973, and thus discovering new ways of thinking and living. This paper explores Comadira’s personal, political and poetic development from 1970 to the years of the Spanish transition to Democracy

Exploiting functional dependencies in declarative problem specifications

Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed in order to express some of the constraints, or due to precise modelling choices, e.g., to provide multiple viewpoints of the search space in order to increase propagation. In either way, the recognition of dependencies greatly helps solvers, letting them avoid spending search on unfruitful branches, while maintaining the highest degree of declarativeness. By modelling constraint problem specifications as second-order formulae, we provide a characterization of functional dependencies in terms of semantic properties of first-order ones. Additionally, we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies. We present opl examples of various problems, from bio-informatics, planning and resource allocation fields, and show how in many cases opl greatly benefits from the addition of such search procedures.