And-inverter graph

About: And-inverter graph is a(n) research topic. Over the lifetime, 1553 publication(s) have been published within this topic receiving 46593 citation(s).

Graph-Based Algorithms for Boolean Function Manipulation

Abstract: In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.

Symbolic Boolean manipulation with ordered binary-decision diagrams

Abstract: Ordered Binary-Decision Diagrams (OBDDs) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satisfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD data structures. Using OBDDs, a wide variety of problems can be solved through symbolic analysis. First, the possible variations in system parameters and operating conditions are encoded with Boolean variables. Then the system is evaluated for all variations by a sequence of OBDD operations. Researchers have thus solved a number of problems in digital-system design, finite-state system analysis, artificial intelligence, and mathematical logic. This paper describes the OBDD data structure and surveys a number of applications that have been solved by OBDD-based symbolic analysis.

The Complexity of Boolean Functions

Abstract: Introduction to the Theory of Boolean Functions and Circuits. The Minimimization of Boolean Functions. The Design of Efficient Circuits for Some Fundamental Functions. Asymptotic Results and Universal Circuits. Lower Bounds on Circuit Complexity. Monotone Circuits. Relations between Circuit Size, Formula Size and Depth. Formula Size. Circuits and other Non-Uniform Computation Methods vs. Turing Machines and other Uniform Computation Models. Hierarchies, Mass Production, and Reductions. Bounded-Depth Circuits. Synchronous, Planar, and Probabilistic Circuits. PRAMs and WRAMs: Parallel Random Access Machines. Branching Programs. References. Index.

Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

Abstract: A Boolean network is a logical dynamic system, which has been used to describe cellular networks. Using a new matrix product, called semi-tensor product of matrices, a logical function can be expressed as an algebraic function. This expression can covert the Boolean networks into discrete-time linear dynamic systems. Similarly, the Boolean control networks can also be converted into discrete time bilinear dynamic systems. Under these forms the standard matrix analysis can be used to consider the structure and the control problems of Boolean (control) networks. After the detailed description of this new approach, the controllability of Boolean control networks is considered in the paper as an application.