Optimal certifying algorithms for linear and lattice point feasibility in a system of UTVPI constraints

This thesis is concerned with the design and analysis of time-optimal and spaceoptimal, certifying algorithms for checking the linear and lattice point feasibility of a class of constraints called Unit Two Variable Per Inequality (UTVPI) constraints. In a UTVPI constraint, there are at most two non-zero variables per constraint, and the coefficients of the non-zero variables belong to the set {lcub}+1, --1{rcub}. These constraints occur in a number of application domains, including but not limited to program verification, abstract interpretation, and operations research. As per the literature, the fastest known certifying algorithm for checking lattice point feasibility in UTVPI constraint systems ([1]), runs in O( m n + n2 log n) time and O(n2) space, where m represents the number of constraints and n represents the number of variables in the constraint system. In this paper, we design and analyze new algorithms for checking the linear feasibility and the lattice point feasibility of UTVPI constraints. Both of the presented algorithms run in O( m[.]n) time and O(m + n) space. Additionally they are certifying in that they produce satisfying assignments in the event that they are presented with feasible instances and refutations in the event that they are presented with infeasible instances. The importance of providing certificates cannot be overemphasized, especially in mission-critical applications. Our approaches for both the linear and the lattice point feasibility problems in UTVPI constraints are fundamentally different from existing approaches for these problems (as described in the literature), in that our approaches are based on new insights on using well-known inference rules

Analyzing Satisfiability and Refutability in Selected Constraint Systems

This dissertation is concerned with the satisfiability and refutability problems for several constraint systems. We examine both Boolean constraint systems, in which each variable is limited to the values true and false, and polyhedral constraint systems, in which each variable is limited to the set of real numbers R in the case of linear polyhedral systems or the set of integers Z in the case of integer polyhedral systems. An important aspect of our research is that we focus on providing certificates. That is, we provide satisfying assignments or easily checkable proofs of infeasibility depending on whether the instance is feasible or not. Providing easily checkable certificates has become a much sought after feature in algorithms, especially in light of spectacular failures in the implementations of some well-known algorithms. There exist a number of problems in the constraint-solving domain for which efficient algorithms have been proposed, but which lack a certifying counterpart. When examining Boolean constraint systems, we specifically look at systems of 2-CNF clauses and systems of Horn clauses. When examining polyhedral constraint systems, we specifically look at systems of difference constraints, systems of UTVPI constraints, and systems of Horn constraints. For each examined system, we determine several properties of general refutations and determine the complexity of finding restricted refutations. These restricted forms of refutation include read-once refutations, in which each constraint can be used at most once; literal-once refutations, in which for each literal at most one constraint containing that literal can be used; and unit refutations, in which each step of the refutation must use a constraint containing exactly one literal. The advantage of read-once refutations is that they are guaranteed to be short. Thus, while not every constraint system has a read-once refutation, the small size of the refutation guarantees easy checkability

O harmonijny rozwój człowieka. Myśl pedagogiczna Profesora Andrzeja Jaczewskiego

Z wprowadzenia: "Andrzej Jaczewski, Profesor Honorowy Krakowskiej Akademii im. Andrzeja Frycza Modrzewskiego w Krakowie, uczony, który we wrześniu b.r. ukończy 90. rok życia, to najstarszy i jeden z nielicznych obecnie autorytetów naukowych w dziedzinie badań nad rozwojem seksualnym dzieci i młodzieży. Jego działalność sytuuje się na pograniczu nauk medycznych i pedagogicznych."(...

sAI

Materiały pornograficzne z udziałem małoletnich (CSAM) stanowią treści audiowizualne, w których prezentowana jest nagość i/lub aktywność wskazująca na kontekst seksualny. Wprowadzenie skutecznego narzędzia informatycznego bazującego na uczeniu maszynowym do identyfikacji oraz klasyfikacji CSAM jest istotne z punktu widzenia seksuologii sądowej. Rozwiązanie takie przyczyni się do wyższej efektywności pracy biegłych z zakresu seksuologii oraz efektywniejszego wykrywania materiałów pornograficznych przez funkcjonariuszy policji. Tworzone w ten sposób narzędzie musi jednak odpowiadać wytycznym Komisji Europejskiej, w tym pozwalać na przedstawienie informacji dotyczącej wyjaśnialności klasyfikacji, która będzie zrozumiała dla ekspertów. Rozwiązanie powinno cechować się również wysoką dokładnością klasyfikacji, trafnością oraz właściwą adaptacją do potrzeb polskiego wymiaru sprawiedliwości. Celem badań było stworzenie narzędzia spełniającego powyższe warunki