A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Abstract

SUMMARYThis paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edgevalued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a measure of subfunctions of f and p is a measure of the rate at which f increases with an increase in the dependent variable. For the special case of an EVMDD, the EVBDD, we show an upper bound on the number of nodes needed to realize an l-restricted Mp-monotone increasing function. Experimental results show that all of the two-variable numeric functions considered in this paper can be converted into an l-restricted Mp-monotone increasing function with p = 1 or 3. Thus, they can be compactly realized by EVBDDs. Since EVMDDs have shorter paths and smaller memory size than EVBDDs, EVMDDs can produce fast and compact NFGs. key words: two-variable numeric function generators (NFGs), edgevalued multiple-valued decision diagrams (EVMDDs), edge-valued binary decision diagrams (EVBDDs), graph-based representation of numeric functions, programmable memory-based architecture

Edge Reduction for EVMDDs to Speed Up Analysis of Multi-state Systems

“…Definition 3: An edge-valued multi-valued decision diagram (EVMDD) [12] is an extension of the MDD [7], [11], and represents a multi-valued function. It consists of one terminal node representing 0 and non-terminal nodes with edges having integer weights; 0-edges always have zero weights.…”

“…In this paper, we propose a new reduction rule for edgevalued MDDs (EVMDDs) [12], [13] to speed up the analysis of MSSs. The existing reduction rules of decision diagrams are intended to reduce redundant nodes, but the proposed rule is intended to reduce redundant edges in EVMDDs.…”

On Optimizations of Edge-Valued MDDs for Fast Analysis of Multi-State Systems

“…An edge-valued MDD (EVMDD) [14] is an extension of the MDD, and represents a multi-valued function. It consists of one terminal node representing 0 and non-terminal nodes with edges having integer weights; 0-edges always have zero weights.…”

“…EVMDDs are known as a compact representation for monotone increasing functions [14]. and an EVMDD for the structure function of Example 1.…”

“…However, minimization of the number of nodes by grouping variables is trivial, and it is not always effective for fast analysis of multi-state systems. Thus, we propose algorithms to minimize the number of edges in an edgevalued multi-valued decision diagram (EVMDD) [14], [15] by grouping multi-valued variables into larger-valued variables. By grouping variables, we can reduce not only the number of edges, but also the number of nodes effectively, resulting in faster analysis of multi-state systems.…”