Boolean function

Abstract: Validation of RTL circuits remains the primary bottleneck in improving design turnaround time, and simulation remains the primary methodology for validation. Simulation-based validation has suffered from a disconnect between the metrics used to measure the error coverage of a set of simulation vectors, and the vector generation process. This disconnect has resulted in the simulation of virtually endless streams of vectors which achieve enhanced error coverage only infrequently. Another drawback has been that most error coverage metrics proposed have either been too simplistic or too inefficient to compute. Recently, an effective observability-based statement coverage metric was proposed along with a fast companion procedure for evaluating it. The contribution of our work is the development of a vector generation procedure targeting the observability-based statement coverage metric. Our method uses repeated coverage computation to minimize the number of vectors generated. For vector generation, we propose a novel technique to set up constraints based on the chosen coverage metric. Once the system of interacting arithmetic and Boolean constraints has been set up, it can be solved using hybrid linear programming and Boolean satisfiability methods. We present heuristics to control the size of the constraint system that needs to be solved. We present experimental results which show the viability of automatically generating vectors using our approach for industrial RTL circuits. We envision our system being used during the design process, as well as during post-design debugging.

Abstract: A two-terminal interactive distributed source coding problem with alternating messages for function computation at both locations is studied. For any number of messages, a computable characterization of the rate region is provided in terms of single-letter information measures. While interaction is useless in terms of the minimum sum-rate for lossless source reproduction at one or both locations, the gains can be arbitrarily large for function computation even when the sources are independent. For a class of sources and functions, interaction is shown to be useless, even with infinite messages, when a function has to be computed at only one location, but is shown to be useful, if functions have to be computed at both locations. For computing the Boolean AND function of two independent Bernoulli sources at both locations, an achievable infinite-message sum-rate with infinitesimal-rate messages is derived in terms of a 2-D definite integral and a rate-allocation curve. The benefit of interaction is highlighted in multiterminal function computation problem through examples. For networks with a star topology, multiple rounds of interactive coding is shown to decrease the scaling law of the total network rate by an order of magnitude as the network grows.

Abstract: This paper presents a theory for (disjunctive and nondisjunctive) function decomposition using the BDD representation of Boolean functions. Incompletely specified as well as multi-output Boolean functions are addressed as part of the general theory. A novel algorithm (based on an EVBDD representation) for generating the set of all bound variables that make the function decomposable is also presented. We compared our BDD-based decomposition procedure with existing implementations of the Roth-Karp procedure and obtained significant speed-ups.