Parameterized complexity of DPLL search procedures

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the running time of parameterized DPLL procedures. We illustrate this technique by showing lower bounds to the parameterized pigeonhole principle and to the ordering principle. As our main application we study the DPLL procedure for the problem of deciding whether a graph has a small clique. We show that proving the absence of a k-clique requires n steps for a non-trivial distribution of graphs close to the critical threshold. For the restricted case of tree-like Parameterized Resolution, this result answers a question asked in [11] of understanding the Resolution complexity of this family of formulas

Proof Complexity of Non-classical Logics.

Proof complexity is an interdisciplinary area of research utilizing techniques from logic, complexity, and combinatorics towards the main aim of understanding the complexity of theorem proving procedures. Traditionally, propositional proofs have been the main object of investigation in proof complexity. Due their richer expressivity and numerous applications within computer science, also non-classical logics have been intensively studied from a proof complexity perspective in the last decade, and a number of impressive results have been obtained. In this paper we give the rst survey of this eld concentrating on recent developments in proof complexity of non-classical logics

Technical means using by Customs administration of the Czech Republic to detection of narcotic and psychoactive drugs.

Autor v úvodu své práce krátce hodnotí vývoj problematiky užívání a zneužívání omamných a psychotropních látek na našem území a popisuje jednotlivé technické prostředky používané v minulosti a současnosti k jejich vyhledávání a detekci. Cílem práce je vymezení způsobu použití technických prostředků v praxi, vhodnosti jejich použití v konkrétních podmínkách výkonu služby a nové trendy ve vývoji a využití těchto prostředků