Investigation of observability property of controlled binary dynamical systems: a logical approach

The property of observability of controlled binary dynamical systems is investigated. A formal definition of the property is given in the language of applied logic of predicates with bounded quantifiers of existence and universality. A Boolean model of the property is built in the form of a quantified Boolean formula accordingly to the Boolean constraints method developed by the authors. This formula satisfies both the logical specification of the property and the equations of the binary system dynamics. Aspects of the proposed approach implementation for the study of the observability property are considered. The technology of checking the feasibility of the property using an applied microservice package is demonstrated in several examples.

A logical method for the synthesis of periodic trajectory in a binary dynamical system

A logic method for structural-parametric synthesis of a binary dynamical system with a given periodic trajectory is proposed. This method provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. All conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. The software implementation of the proposed method in the form of a composite service is presented. All stages of the parametric synthesis of a Boolean network based on the proposed method are demonstrated in the example of a one-step linear system.

Dual Proof Generation for Quantified Boolean Formulas with a BDD-based Solver

Existing proof-generating quantified Boolean formula (QBF) solvers must construct a different type of proof depending on whether the formula is false (refutation) or true (satisfaction). We show that a QBF solver based on ordered binary decision diagrams (BDDs) can emit a single dual proof as it operates, supporting either outcome. This form consists of a sequence of equivalence-preserving clause addition and deletion steps in an extended resolution framework. For a false formula, the proof terminates with the empty clause, indicating conflict. For a true one, it terminates with all clauses deleted, indicating tautology. Both the length of the proof and the time required to check it are proportional to the total number of BDD operations performed. We evaluate our solver using a scalable benchmark based on a two-player tiling game.

Compact Tree Encodings for Planning as QBF

Considerable improvements in the technology and performance of SAT solvers has made their use possible for the resolution of various problems in artificial intelligence, and among them that of generating plans. Recently, promising Quantified Boolean Formula (QBF) solvers have been developed and we may expect that in a near future they become as efficient as SAT solvers. So, it is interesting to use QBF language that allows us to produce more compact encodings. We present in this article a translation from STRIPS planning problems into quantified propositional formulas. We introduce two new Compact Tree Encodings: CTE-EFA based on Explanatory frame axioms, and CTE-OPEN based on causal links. Then we compare both of them to CTE-NOOP based on No-op Actions proposed in [Cashmore et al. 2012]. In terms of execution time over benchmark problems, CTE-EFA and CTE-OPEN always performed better than CTE-NOOP.

Compact Tree Encodings for Planning as QBF

Considerable improvements in the technology and performance of SAT solvers has made their use possible for the resolution of various problems in artificial intelligence, and among them that of generating plans. Recently, promising Quantified Boolean Formula (QBF) solvers have been developed and we may expect that in a near future they become as efficient as SAT solvers. So, it is interesting to use QBF language that allows us to produce more compact encodings. We present in this article a translation from STRIPS planning problems into quantified propositional formulas. We introduce two new Compact Tree Encodings: CTE-EFA based on Explanatory frame axioms, and CTE-OPEN based on causal links. Then we compare both of them to CTE-NOOP based on No-op Actions proposed in [Cashmore et al. 2012]. In terms of execution time over benchmark problems, CTE-EFA and CTE-OPEN always performed better than CTE-NOOP.

Quantified Boolean Formulas: Call the Plumber!

In this tool paper we describe a variation of Nintendo’s Super Mario World dubbed Super Formula World that creates its game maps based on an input quantified Boolean formula. Thus in Super Formula World, Mario, the plumber not only saves his girlfriend princess Peach, but also acts as a QBF solver as a side. The game is implemented in Java and platform independent. Our implementation rests on abstract frameworks by Aloupis et al. that allow the analysis of the computational complexity of a variety of famous video games. In particular it is a straightforward consequence of these results to provide a reduction from QSAT to Super Mario World. By specifying this reduction in a precise way we obtain the core engine of Super Formula World. Similarly Super Formula World implements a reduction from SAT to Super Mario Bros., yielding significantly simpler game worlds.

Solving Stochastic Boolean Satisfiability under Random-Exist Quantification

Stochastic Boolean Satisfiability (SSAT) is a powerful formalism to represent computational problems with uncertainly, such as belief network inference and propositional probabilistic planning. Solving SSAT formulas lies in the same complexity class (PSPACE-complete) as solving Quantified Boolean Formula (QBF). While many endeavors have been made to enhance QBF solving, SSAT has drawn relatively less attention in recent years. This paper focuses on random-exist quantified SSAT formulas, and proposes an algorithm combining binary decision diagram (BDD), logic synthesis, and modern SAT techniques to improve computational efficiency. Unlike prior exact SSAT algorithms, the proposed method can be easily modified to solve approximate SSAT by deriving upper and lower bounds of satisfying probability. Experimental results show that our method outperforms the state-of-the-art algorithm on random k-CNF formulas and has effective application to approximate SSAT on circuit benchmarks.