IEICE TRANSACTIONS on Fundamentals
Super-Set of Permissible Functions and Its Application to the Transduction Method
Summary :
The Transduction Method is a powerful way to design logic circuits, utilizing already existing circuits. A set of permissible functions (SPF) plays an essential role in such circuit transformation/reduction, and is computed at each point (connection or gate output). Currently, two types of SPFs have been used: the maximum SPFs (MSPFs) and compatible SPFs (CSPFs). At each point, the MSPF is literally the set of all PF's, and CSPF is a subset of the MSPF. When CSPFs are calculated, priorities are first assigned to all gates in the circuit. Based on the priorities, it is decided which subset is to be selected as the CSPF. The quality of the results depends on the priorities. In this paper, the concept of super-sets of permissible functions (SSPFs) is introduced to reduce the effect of the priorities that CSPFs depend on. In order to loosen the dependency, each SSPF is computed to contain CSPFs which are candidates to be selected. The experimental results show that the SSPF-based Transduction Method has intermediate reduction capability and takes an intermediate computation time between the MSPF-based and CSPF-based ones. The capability and the time are considered as an acceptably good trade-off. In addition, without any transformations, since SSPFs are the maximum super-set, SSPFs are applicable for analyzing the maximum performance of the CSPF-based transformation, for comparison with the MSPF-based one. Theoretically, the number of connectable gate pairs detected by the MSPFs is 100%. According to the experimental results obtained using SSPFs, on average, 99% are detectable by SSPFs and 1% are detectable only by using the MSPFs. The results show that by using CSPFs, 72% of connectable gate pairs are detectable with any priority assignment and 99% (SSPFs capability) are detectable on average even when the best priorities are assigned. According to the experimental results of CSPF calculation with five priorities, 82% to 93% are practically detectable on average. This is the first quantitative analysis realized by SSPFs which compares the CSPF-based and MSPF-based Transduction Methods with respect to the coverage of PF's.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.12 pp.3124-3133
- Publication Date
- 2004/12/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on VLSI Design and CAD Algorithms)
- Category
- Logic Synthesis
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Katsunori TANAKA, Yahiko KAMBAYASHI, "Super-Set of Permissible Functions and Its Application to the Transduction Method" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 12, pp. 3124-3133, December 2004, doi: .
Abstract: The Transduction Method is a powerful way to design logic circuits, utilizing already existing circuits. A set of permissible functions (SPF) plays an essential role in such circuit transformation/reduction, and is computed at each point (connection or gate output). Currently, two types of SPFs have been used: the maximum SPFs (MSPFs) and compatible SPFs (CSPFs). At each point, the MSPF is literally the set of all PF's, and CSPF is a subset of the MSPF. When CSPFs are calculated, priorities are first assigned to all gates in the circuit. Based on the priorities, it is decided which subset is to be selected as the CSPF. The quality of the results depends on the priorities. In this paper, the concept of super-sets of permissible functions (SSPFs) is introduced to reduce the effect of the priorities that CSPFs depend on. In order to loosen the dependency, each SSPF is computed to contain CSPFs which are candidates to be selected. The experimental results show that the SSPF-based Transduction Method has intermediate reduction capability and takes an intermediate computation time between the MSPF-based and CSPF-based ones. The capability and the time are considered as an acceptably good trade-off. In addition, without any transformations, since SSPFs are the maximum super-set, SSPFs are applicable for analyzing the maximum performance of the CSPF-based transformation, for comparison with the MSPF-based one. Theoretically, the number of connectable gate pairs detected by the MSPFs is 100%. According to the experimental results obtained using SSPFs, on average, 99% are detectable by SSPFs and 1% are detectable only by using the MSPFs. The results show that by using CSPFs, 72% of connectable gate pairs are detectable with any priority assignment and 99% (SSPFs capability) are detectable on average even when the best priorities are assigned. According to the experimental results of CSPF calculation with five priorities, 82% to 93% are practically detectable on average. This is the first quantitative analysis realized by SSPFs which compares the CSPF-based and MSPF-based Transduction Methods with respect to the coverage of PF's.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_12_3124/_p
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@ARTICLE{e87-a_12_3124,
author={Katsunori TANAKA, Yahiko KAMBAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Super-Set of Permissible Functions and Its Application to the Transduction Method},
year={2004},
volume={E87-A},
number={12},
pages={3124-3133},
abstract={The Transduction Method is a powerful way to design logic circuits, utilizing already existing circuits. A set of permissible functions (SPF) plays an essential role in such circuit transformation/reduction, and is computed at each point (connection or gate output). Currently, two types of SPFs have been used: the maximum SPFs (MSPFs) and compatible SPFs (CSPFs). At each point, the MSPF is literally the set of all PF's, and CSPF is a subset of the MSPF. When CSPFs are calculated, priorities are first assigned to all gates in the circuit. Based on the priorities, it is decided which subset is to be selected as the CSPF. The quality of the results depends on the priorities. In this paper, the concept of super-sets of permissible functions (SSPFs) is introduced to reduce the effect of the priorities that CSPFs depend on. In order to loosen the dependency, each SSPF is computed to contain CSPFs which are candidates to be selected. The experimental results show that the SSPF-based Transduction Method has intermediate reduction capability and takes an intermediate computation time between the MSPF-based and CSPF-based ones. The capability and the time are considered as an acceptably good trade-off. In addition, without any transformations, since SSPFs are the maximum super-set, SSPFs are applicable for analyzing the maximum performance of the CSPF-based transformation, for comparison with the MSPF-based one. Theoretically, the number of connectable gate pairs detected by the MSPFs is 100%. According to the experimental results obtained using SSPFs, on average, 99% are detectable by SSPFs and 1% are detectable only by using the MSPFs. The results show that by using CSPFs, 72% of connectable gate pairs are detectable with any priority assignment and 99% (SSPFs capability) are detectable on average even when the best priorities are assigned. According to the experimental results of CSPF calculation with five priorities, 82% to 93% are practically detectable on average. This is the first quantitative analysis realized by SSPFs which compares the CSPF-based and MSPF-based Transduction Methods with respect to the coverage of PF's.},
keywords={},
doi={},
ISSN={},
month={December},}
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TY - JOUR
TI - Super-Set of Permissible Functions and Its Application to the Transduction Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3124
EP - 3133
AU - Katsunori TANAKA
AU - Yahiko KAMBAYASHI
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2004
AB - The Transduction Method is a powerful way to design logic circuits, utilizing already existing circuits. A set of permissible functions (SPF) plays an essential role in such circuit transformation/reduction, and is computed at each point (connection or gate output). Currently, two types of SPFs have been used: the maximum SPFs (MSPFs) and compatible SPFs (CSPFs). At each point, the MSPF is literally the set of all PF's, and CSPF is a subset of the MSPF. When CSPFs are calculated, priorities are first assigned to all gates in the circuit. Based on the priorities, it is decided which subset is to be selected as the CSPF. The quality of the results depends on the priorities. In this paper, the concept of super-sets of permissible functions (SSPFs) is introduced to reduce the effect of the priorities that CSPFs depend on. In order to loosen the dependency, each SSPF is computed to contain CSPFs which are candidates to be selected. The experimental results show that the SSPF-based Transduction Method has intermediate reduction capability and takes an intermediate computation time between the MSPF-based and CSPF-based ones. The capability and the time are considered as an acceptably good trade-off. In addition, without any transformations, since SSPFs are the maximum super-set, SSPFs are applicable for analyzing the maximum performance of the CSPF-based transformation, for comparison with the MSPF-based one. Theoretically, the number of connectable gate pairs detected by the MSPFs is 100%. According to the experimental results obtained using SSPFs, on average, 99% are detectable by SSPFs and 1% are detectable only by using the MSPFs. The results show that by using CSPFs, 72% of connectable gate pairs are detectable with any priority assignment and 99% (SSPFs capability) are detectable on average even when the best priorities are assigned. According to the experimental results of CSPF calculation with five priorities, 82% to 93% are practically detectable on average. This is the first quantitative analysis realized by SSPFs which compares the CSPF-based and MSPF-based Transduction Methods with respect to the coverage of PF's.
ER -
English
