The open problem in knowledge compilation of whether the language PI is at least as succinct as MODS is answered in the negative. For this purpose a class of Boolean functions with a number of prime implicants that is superpolynomial in their number of false points is constructed. A lower bound (proving that PI is not at least as succinct as MODS), an upper bound (proving that the counterexample cannot yield an exponential separation of PI and MODS) and the precise number of the prime implicants of these functions is computed. Powered by TCPDF (www.tcpdf.org)

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state and state transitions. While few practical problems are purely conformant, the ability to find conformant plans is needed in planning with observations where conformant situations are an special case and where relaxations into conformant planning yield useful heuristics. In this dissertation, we introduce new formulations for tackling the conformant planning problem with deterministic actions using translations. On the one hand, we propose a translation in propositional logic and two schemes for obtaning conformant plans for it, one based on boolean operations of projection and model counting, the other based on projection and satisfiability. On the other hand, we introduce translations of the conformant planning problem into classical problems that are solved by a modern and effective classical planner. We analyze the formal properties of the translations into classical planning and evaluate the performance of the resulting conformant planners. / La planificación conformante es el problema de encontrar una secuencia de acciones para lograr un objetivo en presencia de información incompleta sobre el estado inicial y en las transiciones entre estados. Aunque pocos problemas son de carácter puramente conformante, la posibilidad de encontrar planes conformantes es necesaria en planificación con observaciones, donde las situaciones conformantes son un caso particular, y donde las relajaciones a planificación conformante dan heurísticas útiles. En esta tesis atacamos el problema de la planificación conformante con acciones determinísticas mediante dos formulaciones basadas en traducciones. Por un lado, proponemos una traducción a lógica proposicional y dos esquemas para obtener planes conformantes a partir de ésta, uno basado en operaciones booleanas de projección y conteo de modelos, y otro basado en projección y satisfacción proposicional. Por otro lado, introducimos traducciones que permiten transformar un problema de planificación conformante en un problema de planificación clásica que es luego resuelto usando planificadores clásicos. También analizamos las propiedades formales de las traducciones y evaluamos el rendimiento de los planificadores obtenidos.

An NNF circuit is a directed acyclic graph (DAG), where each leaf is labelled with either true/false or a literal, and each inner node represents either a conjunction (∧) or a disjunction (∨). A decomposable NNF (DNNF) is an NNF satisfying the decomposabi- lity property for each conjunction node. The C-BDMC language generalizes the DNNF language. In a C-BDMC, the leaves can contain CNF formulae from a given base class C. In this paper, we focus only on renamable Horn formulae. We experimentally compare the sizes of d-BDMC and d-DNNF representations. We describe a new compilation langu- age, called cara DNNF (c-DNNF), that generalizes the DNNF language. A c-DNNF circuit can be considered as a compressed representation of a DNNF circuit. We present a new experimental knowledge compiler, called CaraCompiler, for converting a CNF formula into a d-BDMC or a (c)d-DNNF circuit. CaraCompiler is based on the state-of-the-art compiler D4. Also, we mention some extensions for the compiler D4, such as caching hypergraph cuts that can reduce the compilation times. 1

Title: Boolean techniques in Knowledge representation Author: Miloš Chromý Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: Doc. RNDr. Ondřej Čepek, Ph.D., Department of Theoretical Com- puter Science and Mathematical Logic Abstract: In this thesis we will investigate switch-list representations of Boolean function and we will explore the biclique satisfiable formulas. Given a truth table representation of a Boolean function f the switch-list rep- resentation of f is a list of Boolean vectors from the truth table which have a different function value than the preceding Boolean vector in the truth table. We include this type of representation in the Knowledge Compilation Map [Dar- wiche and Marquis, 2002] and argue that switch-lists may in certain situations constitute a reasonable choice for a target language in knowledge compilation. First, we compare switch-list representations with a number of standard repre- sentations (such as CNF, DNF, and OBDD) with respect to their relative suc- cinctness. As a by-product of this analysis we also give a short proof of a long standing open question from [Darwiche and Marquis, 2002], namely the incom- parability of MODS (models) and PI (prime implicates) representations. Next, using the succinctness result between...