On Using Satisfiability-Based Pruning Techniques in Covering Algorithms

Covering problems are widely used as a modeling tool in Electronic Design Automation (EDA). Recent years have seen dramatic improvements in algorithms for the Unate/Binate Covering Problem (UCP/BCP). Despite these improvements, BCP is a well-known computationally hard problem, with many existing real-world instances that currently are hard or even impossible to solve. In this paper we apply search pruning techniques from the Boolean Satisfiability (SAT) domain to BCP. Furthermore, we generalize these techniques, in particular the ability to backtrack nonchronologically, to exploit the actual formulation of covering problems. Experimental results, obtained on representative instances of the Unate and Binate Covering Problems, indicate that the proposed techniques provide significant performance gains for different classes of instances. 1. Introduction The Binate Covering Problem (BCP) finds many applications in Electronic Design Automation (EDA), examples of which include logic and se..

Constraint solving over multi-valued logics - application to digital circuits

Due to usage conditions, hazardous environments or intentional causes, physical and virtual systems are subject to faults in their components, which may affect their overall behaviour. In a ‘black-box’ agent modelled by a set of propositional logic rules, in which just a subset of components is externally visible, such faults may only be recognised by examining some output function of the agent. A (fault-free) model of the agent’s system provides the expected output given some input. If the real output differs from that predicted output, then the system is faulty. However, some faults may only become apparent in the system output when appropriate inputs are given. A number of problems regarding both testing and diagnosis thus arise, such as testing a fault, testing the whole system, finding possible faults and differentiating them to locate the correct one. The corresponding optimisation problems of finding solutions that require minimum resources are also very relevant in industry, as is minimal diagnosis. In this dissertation we use a well established set of benchmark circuits to address such diagnostic related problems and propose and develop models with different logics that we formalise and generalise as much as possible. We also prove that all techniques generalise to agents and to multiple faults. The developed multi-valued logics extend the usual Boolean logic (suitable for faultfree models) by encoding values with some dependency (usually on faults). Such logics thus allow modelling an arbitrary number of diagnostic theories. Each problem is subsequently solved with CLP solvers that we implement and discuss, together with a new efficient search technique that we present. We compare our results with other approaches such as SAT (that require substantial duplication of circuits), showing the effectiveness of constraints over multi-valued logics, and also the adequacy of a general set constraint solver (with special inferences over set functions such as cardinality) on other problems. In addition, for an optimisation problem, we integrate local search with a constructive approach (branch-and-bound) using a variety of logics to improve an existing efficient tool based on SAT and ILP