We identify two families of canonical representations called ROBDD[∧î]C and ROBDD[∧T̂ ,i]T by augmenting ROBDD with two types of conjunctive decompositions. These representations cover the three existing languages ROBDD, ROBDD with as many implied literals as possible (ROBDDL∞), and AND/OR BDD. We introduce a new time efficiency criterion called rapidity which reflects the idea that exponential ...

This paper augments OBDD with conjunctive decomposition to propose a generalization called OBDD[∧]. By imposing reducedness and the finest ∧-decomposition bounded by integer i (∧î-decomposition) on OBDD[∧], we identify a family of canonical languages called ROBDD[∧î], where ROBDD[∧0̂] is equivalent to ROBDD. We show that the succinctness of ROBDD[∧î] is strictly increasing when i increases. We i...

Despite the ubiquity of ROBDDs in program analysis, and extensive literature on ROBDD minimisation, there is a dearth of work on approximating ROBDDs. The need for approximation arises because many ROBDD operations result in an ROBDD whose size is quadratic in the size of the inputs. Furthermore, if ROBDDs are used in abstract interpretation, the running time of the analysis is related not only...

The goal of this work is to describe a new algorithm for finding the optimal variable order, number of nodes for any order and other ROBDD parameters, based on a tabular method. The tabular method makes use of a pre-built backend database table that stores the ROBDD size for selected combinations of min-terms. The user uses the backend table and the proposed algorithm to find the necessary ROBD...

A binary string of length 2 induces the Boolean function of k variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The given binary string is fully recoverable from this ROBDD. We exhibit a lossless data compression algorithm in which a binary string of length a power of two is com...

The paper presents logical derivation algorithms that can be applied to inversion of polynomially computable discrete functions. The proposed approach is based on the fact that it is possible to organize DPLL derivation on a small subset of variables appeared in a CNF which encodes the algorithm computing the function. The experimental results showed that arrays of conflict clauses generated by...

The most common way to build the reduced ordered binary decision diagram (ROBDD) of a complex gate (or function) f of a network is bottom-up, i.e., by rst building the ROBDDs of the sub-expressions of f and then suitably combining them. Such a method, however, has been found to su er from memory explosion, even when the ROBDD of f is not large. This leads to the following fundamental question: ...

Reduced Ordered Binary Decision Diagrams (ROB-DDs), also known as Bryant graphs, are a representation for Boolean functions supporting many eecient operations. Because of this, they have often been used to implement the positive Boolean functions for program analysis. Some ROBDD operations heavily used in program analysis, however, are still rather expensive. The undertaking of the present pape...

ROBDDs have traditionally been built in a bottom-up fashion, through the recursive use of Bryant's apply procedure [6], or the ITE [4] procedure. With these methods, the peak memory utilization is often larger than the nal ROBDD size. Though methods like Dynamic Variable Reordering [21] have been proposed to reduce the memory utilization, such schemes have an associated time penalty. In this pa...

This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...