We propose novel algorithms for design and design space exploration. The designs computed by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified satisfiability and use advanced solvers to find solutions that represent useful systems. The algorithms we present in this paper are sound and complete and are guaranteed to discover correct designs of optimal size, if they exist. We apply our method to the design of Boolean systems and discover new and more optimal classical and quantum circuits for common arithmetic functions such as addition and multiplication. The performance of our algorithms is evaluated through extensive experimentation. We have first created a benchmark consisting of specifications of scalable synthetic digital circuits and real-world mirochips. We have then generated multiple circuits functionally equivalent to the ones in the benchmark. The quantified satisfiability method shows more than four orders of magnitude speed-up, compared to a generate and test method that enumerates all non-isomorphic circuit topologies. Our approach generalizes circuit optimization. It uses arbitrary component libraries and has applications to areas such as digital circuit design, diagnostics, abductive reasoning, test vector generation, and combinatorial optimization.

A known limitation of many diagnosis algorithms is that the number of diagnoses they return can be very large. This raises the question of how to use such a large set of diagnoses. For example, presenting hundreds of diagnoses to a human operator (charged with repairing the system) is meaningless. In various settings, including decision support for a human operator and automated troubleshooting processes, it is sufficient to be able to answer a basic diagnostic question: is a given component faulty? We propose a way to aggregate an arbitrarily large set of diagnoses to return an estimate of the likelihood of a given component to be faulty. The resulting mapping of components to their likelihood of being faulty is called the system's health state. We propose two metrics for evaluating the accuracy of a health state and show that an accurate health state can be found without finding all diagnoses. An empirical study explores the question of how many diagnoses are needed to obtain an accurate enough health state, and a simple online stopping criterion is proposed.

Fault diagnosis of analogue linear systems poses many challenges, such as the size of the search space that must be explored and the possibility of simulation instabilities introduced by particular fault classes. We study a novel algorithm that addresses both problems. This algorithm dynamically modifies the simulation model during diagnosis by pruning parametrized components that cause discontinuity in the model. We provide a theoretical framework for predicting the speedups, which depends on the topology of the model. We empirically validate the theoretical predictions through extensive experimentation on a benchmark of circuits.

Therefore, diagnostic algorithms must reason backwards from symptoms to causes. For example, determining that a dead battery is the cause of your car not starting in the morning (and not the wiring or the ignition switch). The domains of diagnostic algorithms includes analog and digital circuits, software systems, thermal systems, biological systems, and physical mechanisms. The same classes of diagnostic algorithms can apply in all domains. Diagnostic algorithms make observations, often in real time, of a system being diagnosed.

Multi-level logic synthesis is a problem of immense practical significance, and is a key to developing circuits that optimize a number of parameters, such as depth, energy dissipation, reliability, etc. The problem can be defined as the task of taking a collection of components from which one wants to synthesize a circuit that optimizes a particular objective function. This problem is computationally hard, and there are very few automated approaches for its solution. To solve this problem we propose an algorithm, called Circuit-Decomposition Engine (CDE), that is based on learning decision trees, and uses a greedy approach for function learning. We empirically demonstrate that CDE, when given a library of different component types, can learn the function of Disjunctive Normal Form (DNF) Boolean representations and synthesize circuit structure using the input library. We compare the structure of the synthesized circuits with that of well-known circuits using a range of circuit similarity metrics.

A model-based diagnosis problem occurs when an observation is inconsistent with the assumption that the diagnosed system is not faulty. The task of a diagnosis engine is to compute diagnoses, which are assumptions on the health of components in the diagnosed system that explain the observation. In this paper, we extend Reiter's well-known theory of diagnosis by exploiting the duality of the relation between conflicts and diagnoses. This duality means that a diagnosis is a hitting set of conflicts, but a conflict is also a hitting set of diagnoses. We use this property to interleave the search for diagnoses and conflicts: a set of conflicts can guide the search for diagnosis, and the computed diagnoses can guide the search for more conflicts. We provide the formal basis for this dual conflict-diagnosis relation, and propose a novel diagnosis algorithm that exploits this duality. Experimental results show that the new algorithm is able to find a minimal cardinality diagnosis faster than the well-known Conflict-Directed A*.