Spectral transforms for large boolean functions with applications to technology mapping

Clarke, Edmund M.; McMillan, Kenneth L.; Zhao, Xudong; Fujita, Masahiro; Yang, Joshua

doi:10.1145/157485.164569

Cited by 212 publications

(132 citation statements)

References 5 publications

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“…Schrammel (2013) proposes two of such compositions to actually abstract concrete domains comprising both Boolean (B n ) and numerical (V m ) components: In practice, product domains can be implemented with a combination of binary decision diagrams and classical numerical abstract domains. Also, as multi-terminal binary decision diagrams (Clarke et al, 1993) can be used to describe functions in the form of B n → D (for any D whose elements can be represented in a canonical way), this kind of structure is suitable to the implementation of power abstract domains.…”

Section: Over-approximating Logico-numerical State Spacesmentioning

confidence: 99%

Discrete Controller Synthesis for Infinite State Systems with ReaX

Berthier

Marchand

2014

IFAC Proceedings Volumes

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Section: Over-approximating Logico-numerical State Spacesmentioning

confidence: 99%

Discrete Controller Synthesis for Infinite State Systems with ReaX

Berthier

Marchand

2014

IFAC Proceedings Volumes

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“…For more detail on definitions and reduction rules, see [8], [27], [37]. Definition 5: A multi-terminal binary decision diagram (MTBDD) [6] is an extension of a BDD [3], [17], and represents an integer-valued function. In the MTBDD, the terminal nodes are labeled by integers.…”

Section: Decision Diagramsmentioning

confidence: 99%

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

Nagayama

Sasao

Butler

2010

IEICE Trans. Inf. & Syst.

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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

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“…They are based on the canonical representation of the binary tree of the function as a directed graph obtained through folding internal nodes representing identical subfunctions (subject to an ordering of the variables to guarantee uniqueness of the representation) and using 0 and 1 as leaves. In [16] it is shown how one can generalize BDDs to cogently and efficiently represent matrices in terms of so-called multi-terminal binary decision diagrams (MTBDDs).…”

Section: Multi-terminal Binary Decision Diagramsmentioning

confidence: 99%

“…Despite the power of existing linear algebra packages, this can lead to inefficient and time consuming computation through the implicit requirement for the construction of the state space. This paper proposes an alternative, which is based on expressing the probability calculations in terms of Multi-Terminal Binary Decision Diagrams (MTBDDs) [16]. MTBDDs are a generalization of (ordered) BDDs in the sense that they allow arbitrary real numbers in the terminal nodes instead of just 0 and 1, and so can provide a compact representation for matrices.…”

Section: Introductionmentioning

confidence: 99%

Symbolic model checking for probabilistic processes

Baier

Clarke

Hartonas-Garmhausen

et al. 1997

Automata, Languages and Programming

110

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Abstract.We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by Multi-Terminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas and MTBDDs to represent Markov chains, and is efficient because it avoids explicit state space construction. A PCTL model checker is being implemented in Verus [9].

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Spectral transforms for large boolean functions with applications to technology mapping

Cited by 212 publications

References 5 publications

Discrete Controller Synthesis for Infinite State Systems with ReaX

Discrete Controller Synthesis for Infinite State Systems with ReaX

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

Symbolic model checking for probabilistic processes

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