INTRODUCTION Two level logic minimization crucial in VLSI design

1. Iterated Invocation of ESPRESSO for Two – Level Logic Minimization Prince VargheseDr. Sunil Khatri (Faculty Mentor), CharuNagpal (Graduate Student Advisor) ABSTRACT Two – level logic minimization is a key procedure in VLSI logic optimization. The most practical approach is ESPRESSO. In most cases ESPRESSO returns the exact minimum solution in a fraction of the time required for exact two-level minimization (Quine-McCluskey). In 2004 an approach was developed to further improve the results of ESPRESSO, using an iterated invocation of ESPRESSO. In this work, we reimplementthe results of this iterative procedure. Our results show that in 18 of the 53 cases, we can further improve the results of ESPRESSO, with a modest Increase in run time. • Iterate the invocation of ESPRESSO • > User specifies the number of iterations p. In • each iteration i, remove a set of “best” cubes • {Ci}. In subsequent iterations, {Ci} is treated as • Don’t cares. • Final result is U{Ci} • We explore three varieties of this basic idea (Black, Blue, • and Red) • In each iteration i, remove k cubes, where k is the • smallest integer satisfying : • n • p + 1 - i = k • where n is the number of cubes in the cover. • Best cubes {Ci} are selected based on one of the two • methods: • > SIZE : Sort cubes in descending order of size • and assign the k largest cubes to {Ci}. • > DISTANCE : Sort cubes in ascending order of • their total distance to the other cubes in the • cover. Assign first k cubes to {Ci}. APPROACH BLACK VARIANT BLUE VARIANT RED VARIANT • INTRODUCTION • Two level logic minimization crucial in VLSI design • >Helps simplify logic before Technology Dependent Optimization • Traditional Methods • >Quine-McCluskey (Exact) • >Iterated Consensus ( Heuristic) • >ESPRESSO (Heuristic) • Most practical method is ESPRESSO (extremely fast, results close • to optimal) • >Hard to improve( in about 65% of cases ESPRESSO already • produces exact minimum solution) • Can we improve ESPRESSO results further? RESULTS FOR BLACK ALGORITHM RESULTS Out of 154 examples, only 53 were improvable. The results for the Black algorithm is shown in the table to the right. A table showing the number of example cases won and the sum of cubes by which the algorithm won is given below. REDUCE Local minimum EXPAND IRREDUNDANT Local minimum ESPRESSO ILLUSTRATED The number of examples where each variant won over ESPRESSO and the sum of cubes by which they won Plot of Iteration number vs. Time for Black Size Algorithm (from previous Implementation) • Department of Electrical and Computer Engineering • Texas A&M University College Station, TX 77843-3128 Electrical Engineering Research Applications to Homeland Security National Science Foundation Research Experiences for Undergraduates