Jordan Gergov

Efficient Boolean manipulation with OBDD's can be extended to FBDD's

OBDDs are the state-of-the-art data structure for Boolean function manipulation. Basic tasks of Boolean manipulation such as equivalence test, satisfiability test, tautology test and single Boolean synthesis steps can be performed efficiently in terms of fixed ordered OBDDs. The bottleneck of most OBDD-applications is the size of the represented Boolean functions since the total computation merely remains tractable as long as the OBDD-representations remain of reasonable size. Since it is well known that OBDDs are restricted FBDDs (free BDDs, i.e., BDDs that test, on each path, each input variable at most once), and that FBDD-representations are often much more (sometimes even exponentially more) concise than OBDD-representations. We propose to work with a more general FBDD-based data structure. We show that FBDDs of a fixed type provide, similar as OBDDs of a fixed variable ordering, canonical representations of Boolean functions, and that basic tasks of Boolean manipulation can be performed in terms of fixed typed FBDDs similarly efficient as in terms of fixed ordered OBDDs. In order to demonstrate the power of the FBDD-concept we show that the verification of the circuit design for the hidden weighted bit function proposed Bryant can be carried out efficiently in terms of FBDDs while this is, for principal reasons, impossible in terms of OBDDs. >

Frontiers of Feasible and Probabilistic Feasible Boolean Manipulation with Branching Programs

A central issue in the solution of many computer aided design problems is to find concise representations for circuit designs and their functional specification. Recently, a restricted type of branching programs (OB-DDs) proved to be extremely useful for representing Boolean functions for various CAD applications [Bry92]. Unfortunatelly, many circuits of practical interest provably require OBDD-representations of exponential size. In the following we systematically study the question up to what extend more concise BP-representations can be successfully used in symbolic Boolean manipulation, too. We prove, in very general settings,

Boolean manipulation with free BDD's. First experimental results

It is shown that Free Binary Decision Diagrams (FBDDs), with respect to a predefined type, provide a canonical representation and allow efficient solutions of the basic tasks in Boolean manipulation in a similar manner to the well-known OBDDs. However, in contrast to OBDDs, the FBDDs allow more succinct representations of Boolean functions. For experimentation we have used an FBDD-package and the types worked with are tree-based. Using different type-creating heuristics, we compare the size of FBDD-representations of some ISCAS benchmarks with the size of their OBDD-representations.<<ETX>>

Analysis and Manipulation of Boolean Functions in Terms of Decision Graphs

We investigate the question whether and to what extend the solution of central tasks of digital logic circuit design of a given Boolean function f benefits from a representation of f in terms of certain restricted decision graphs or branching programs.

On the complexity of analysis and manipulation of Boolean functions in terms of decision graphs

* Corresponding author. Email: meinel@uni-trier.de. investigations of alternative representations for logic functions. Well studied and of great importance in circuit design are two-level normal forms such as the disjunctive (DNF) or the conjunctive normal firm (CNF). I n circuit theory multi-level representations, such as Boolean formulas or circuits have found considerable importance. Although, due to an easy counting argument, for each of the mentioned types of representations almost all Boolean functions require representations of exponential length many functions of practical interest possess at least succinct (i.e. polynomial length) circuit representations. Unfortunately, it is rather difficult to analyse and manipulate Boolean functions that are represented by Boolean circuits. For that reason in computeraided circuit design one is interested in other representations that are, on the one hand, more succinct than two-level representations and, on the other hand, easier to analyse and manipulate than Boolean circuits. One candidate which seems to satisfy these two conditions is the concept of decision graphs or branching programs. Branching programs,