Ordered Binary-Decision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD

We describe a technique for verifying the control logic of pipelined microprocessors. It handles more complicated designs, and requires less human intervention, than existing methods. The technique automaticMly compares a pipelined implementation to an architectural description. The CPU time needed for verification is independent of the data path width, the register file size, and the number of ALU operations.

The temporal logic model checking algorithm of Clarke, Emerson, and Sistla [17] is modified to represent state graphs using binary decision diagrams (BDD’s) [7] and partitioned trunsirion relations [lo], 1111. Because this representation captures some of the regularity in the state space of circuits with data path logic, we are able to verify circuits with an extremely large number of states. We demonstrate this new technique on a synchronous pipelined design with approximately 5 x 10^120 states. Our model checking algorithm handles full CTL with fairness constraints. Consequently, we are able to express a number of important liveness and fairness properties, which would otherwise not be expressible in CTL. We give empirical results on the performance of the algorithm applied to both synchronous and asynchronous circuits with data path logic.

With the advent of portable and high-density microelectronic devices, the power dissipation of very large scale integrated (VLSI) circuits is becoming a critical concern. Accurate and efficient power estimation during the design phase is required in order to meet the power specifications without a costly redesign process. In this paper, we present a review/tutorial of the power estimation techniques that have recently been proposed. Invited, IEEE Trans. on VLSI, Dec. 1994. 1. Introduction The continuing decrease in feature size and the corresponding increase in chip density and operating frequency have made power consumption a major concern in VLSI design [1, 2]. Modern microprocessors are indeed hot: the PowerPC chip from Motorola consumes 8.5 Watts, the Pentium chip from Intel consumes 16 Watts, and DEC's alpha chip consumes 30 Watts. Excessive power dissipation in integrated circuits not only discourages their use in a portable environment, but also causes overheating, which degr...

The CUDD package provides functions to manipulate Binary Decision Diagrams (BDDs) [5,3], Algebraic Decision Diagrams (ADDs) [1], and Zero suppressed Decision Diagrams (ZDDs) [12]. BDDs are used to represent switch functions

We significantly reduce the complexity of BDD-based symbolic verification by using partitioned transition relations to represent state transition graphs. This method can be applied to both synchronous and asynchronous circuits. The times necessary to verify a synchronous pipeline and an asynchronous stack are both bounded by a low polynomial in the size of the circuit. We were able to handle stacks with over 10 50 reachable states and pipelines with over 10 120 reachable states. 1 Introduction Although methods for verifying sequential circuits by searching their state transition graphs have been investigated for many years, it is only recently that such methods have begun to seem practical. Before, the largest circuits that could be verified had about 10 6 states. Now it is easy to check circuits that have many orders of magnitude more states [3, 5, 6, 7]. The reason for the dramatic increase is the use of special data structures such as binary decision diagrams (BDDs) [2] for...

Reliability assessment is an important part of the design process of digital integrated circuits. We observe that a common thread that runs through most causes of run-time failure is the extent of circuit activity, i.e., the rate at which its nodes are switching. We propose a new measure of activity, called the transition density, which may be defined as the "average switching rate" at a circuit node. Based on a stochastic model of logic signals, we also present an algorithm to propagate density values from the primary inputs to internal and output nodes. To illustrate the practical significance of this work, we demonstrate how the density values at internal nodes can be used to study circuit reliability by estimating (1) the average power & ground currents, (2) the average power dissipation, (3) the susceptibility to electromigration failures, and (4) the extent of hot-electron degradation. The density propagation algorithm has been implemented in a prototype density simulator. Using ...

Temporal logic model checking is an automatic technique for verifying finite-state concurrent systems. Specifications are expressed in a propositional temporal logic, and the concurrent system is modeled as a state-transition graph. An efficient search procedure is used to determine whether or not the state-transition graph satisfies the specification. When the technique was first developed ten years ago, it was only possible to handle concurrent systems with a few thousand states. In the last few years, however, the size of the concurrent systems that can be handled has increased dramatically. By representing transition relations and sets of states implicitly using binary decision diagrams, it is now possible to check concurrent systems with more than 10 120 states. In this paper we describe in detail how the new implementation works and

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We show how LTL model checking can be reduced to CTL model checking with fairness constraints. Using this reduction, we also describe how to construct a symbolic LTL model checker that appears to be quite efficient in practice. In particular, we show how the SMV model checking system developed by McMillan [16] can be extended to permit LTL specifications. The results that we have obtained are quite surprising. For the examples we considered, the LTL model checker required at most twice as much time and space as the CTL model checker. Although additional examples still need to be tried, it appears that efficient LTL model checking is possible when the specifications are not excessively complicated. This research was sponsored in part by the Avionics Laboratory, Wright Research and Development Center, Aeronautical Systems Division (AFSC), U.S. Air Force, Wright-Patterson AFB, Ohio 45433-6543 under Contract F33615-90-C-1465, ARPA Order No. 7597 and in part by the National Science foundat...