CNF-SAT modelling for banyan-type networks and its application for assessing the rearrangeability

A banyan-type network is a switching network, which is constructed by placing unit switches with two inputs and two outputs in s (s > 1) stages. In each stage, 2 n – 1 (n > 1) unit switches are aligned. Past studies conjecture that this network becomes rearrangeable when s ≥ 2n-1. Although a considerable number of theoretical analyses have been done, the rearrangeability of the banyan-type network with 2n – 1 or more stages is not completely proved. As a tool to assess the rearrangeability, this study presents a CNF-SAT (conjunctive normal form - satisfiability) modelling scheme for banyan-type networks. In the proposed scheme, the routing is formulated to a SAT problem represented in CNF. By feeding the problem to a SAT solver, it is found whether the problem is satisfiable or unsatisfiable. If the problem is unsatisfiable for a certain request, the network is not rearrangeable. By contrast, if the problem is satisfiable for any requests, the network is rearrangeable. This study applies the CNF-SAT modelling scheme to various configurations of 2n – 1 stage banyan-type networks. These networks are assessed for rearrangeability by solving the SAT problems. The proposed method will be helpful to conduct future theoretical studies on banyan-type networks.

Learning First-Order Representations for Planning from Black Box States: New Results

Recently Bonet and Geffner have shown that first-order representations for planning domains can be learned from the structure of the state space without any prior knowledge about the action schemas or domain predicates. For this, the learning problem is formulated as the search for a simplest first-order domain description D that along with information about instances I_i (number of objects and initial state) determine state space graphs G(P_i) that match the observed state graphs G_i where P_i = (D, I_i). The search is cast and solved approximately by means of a SAT solver that is called over a large family of propositional theories that differ just in the parameters encoding the possible number of action schemas and domain predicates, their arities, and the number of objects. In this work, we push the limits of these learners by moving to an answer set programming (ASP) encoding using the CLINGO system. The new encodings are more transparent and concise, extending the range of possible models while facilitating their exploration. We show that the domains introduced by Bonet and Geffner can be solved more efficiently in the new approach, often optimally, and furthermore, that the approach can be easily extended to handle partial information about the state graphs as well as noise that prevents some states from being distinguished.

Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) for obtaining a propositional abstraction of the QBF. If this formula is false, the truth value of the QBF is decided, otherwise further refinement steps are necessary. Classically, expansion-based solvers process the given formula quantifier-block wise and use one SAT solver per quantifier block. In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided and only two incremental SAT solvers are required. While our algorithm is naturally based on the $$\forall $$ ∀ Exp+Res calculus that is the formal foundation of expansion-based solving, it is conceptually simpler than present recursive approaches. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.

Skeptical Reasoning with Preferred Semantics in Abstract Argumentation without Computing Preferred Extensions

We address the problem of deciding skeptical acceptance wrt. preferred semantics of an argument in abstract argumentation frameworks, i.e., the problem of deciding whether an argument is contained in all maximally admissible sets, a.k.a. preferred extensions. State-of-the-art algorithms solve this problem with iterative calls to an external SAT-solver to determine preferred extensions. We provide a new characterisation of skeptical acceptance wrt. preferred semantics that does not involve the notion of a preferred extension. We then develop a new algorithm that also relies on iterative calls to an external SAT-solver but avoids the costly part of maximising admissible sets. We present the results of an experimental evaluation that shows that this new approach significantly outperforms the state of the art. We also apply similar ideas to develop a new algorithm for computing the ideal extension.

On Explaining Random Forests with SAT

Random Forest (RFs) are among the most widely used Machine Learning (ML) classifiers. Even though RFs are not interpretable, there are no dedicated non-heuristic approaches for computing explanations of RFs. Moreover, there is recent work on polynomial algorithms for explaining ML models, including naive Bayes classifiers. Hence, one question is whether finding explanations of RFs can be solved in polynomial time. This paper answers this question negatively, by proving that computing one PI-explanation of an RF is D^P-hard. Furthermore, the paper proposes a propositional encoding for computing explanations of RFs, thus enabling finding PI-explanations with a SAT solver. This contrasts with earlier work on explaining boosted trees (BTs) and neural networks (NNs), which requires encodings based on SMT/MILP. Experimental results, obtained on a wide range of publicly available datasets, demonstrate that the proposed SAT-based approach scales to RFs of sizes common in practical applications. Perhaps more importantly, the experimental results demonstrate that, for the vast majority of examples considered, the SAT-based approach proposed in this paper significantly outperforms existing heuristic approaches.