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This paper describes the proof calculus LD for clausal propositional logic, which is a linearized form of the well-known DPLL calculus extended by clause learning. It is motivated by the demand to model how current SAT solvers built on clause learning are working, while abstracting from decision heuristics and implementation details. The calculus is proved sound and terminating. Further, it is shown that both the original DPLL calculus and the conflict-directed backtracking calculus with clause learning, as it is implemented in many current SAT solvers, are complete and proof-confluent instances of the LD calculus.
Many formal descriptions of DPLL-based SAT algorithms either do not include all essential proof techniques applied by modern SAT solvers or are bound to particular heuristics or data structures. This makes it difficult to analyze proof-theoretic properties or the search complexity of these algorithms. In this paper we try to improve this situation by developing a nondeterministic proof calculus that models the functioning of SAT algorithms based on the DPLL calculus with clause learning. This calculus is independent of implementation details yet precise enough to enable a formal analysis of realistic DPLL-based SAT algorithms.
We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.
TrainTrap
(2020)
Companies develop process models to explicitly describe their business operations. In the same time, business operations, business processes, must adhere to various types of compliance requirements. Regulations, e.g., Sarbanes Oxley Act of 2002, internal policies, best practices are just a few sources of compliance requirements. In some cases, non-adherence to compliance requirements makes the organization subject to legal punishment. In other cases, non-adherence to compliance leads to loss of competitive advantage and thus loss of market share. Unlike the classical domain-independent behavioral correctness of business processes, compliance requirements are domain-specific. Moreover, compliance requirements change over time. New requirements might appear due to change in laws and adoption of new policies. Compliance requirements are offered or enforced by different entities that have different objectives behind these requirements. Finally, compliance requirements might affect different aspects of business processes, e.g., control flow and data flow. As a result, it is infeasible to hard-code compliance checks in tools. Rather, a repeatable process of modeling compliance rules and checking them against business processes automatically is needed. This thesis provides a formal approach to support process design-time compliance checking. Using visual patterns, it is possible to model compliance requirements concerning control flow, data flow and conditional flow rules. Each pattern is mapped into a temporal logic formula. The thesis addresses the problem of consistency checking among various compliance requirements, as they might stem from divergent sources. Also, the thesis contributes to automatically check compliance requirements against process models using model checking. We show that extra domain knowledge, other than expressed in compliance rules, is needed to reach correct decisions. In case of violations, we are able to provide a useful feedback to the user. The feedback is in the form of parts of the process model whose execution causes the violation. In some cases, our approach is capable of providing automated remedy of the violation.