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Oneinputface MPCVP is Hard for L, but in LogDCFL
"... A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that ev ..."
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A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the oneinputface MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted oneinputface MPCVP is also in LogDCFL. We also show this problem to be Lhard under quantifier free projections.
Formal Modeling and Analysis of an Audio/Video Protocol: An Industrial . . .
, 1997
"... A formal and automatic verification of a reallife protocol is presented. The protocol, about 2800 lines of assembler code, has been used in products from the audio/video company Bang & Olufsen throughout more than a decade, and its purpose is to control the transmission of messages between a ..."
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A formal and automatic verification of a reallife protocol is presented. The protocol, about 2800 lines of assembler code, has been used in products from the audio/video company Bang & Olufsen throughout more than a decade, and its purpose is to control the transmission of messages between audio/video components over a single bus. Such communications may collide, and one essential purpose of the protocol is to detect such collisions. The functioning is highly dependent on realtime considerations. Though the protocol was known to be faulty in that messages were lost occasionally, the protocol was too complicated in order for Bang & Olufsen to locate the bug using normal testing. However, using the realtime verification tool UPPAAL, an error trace was automatically generated, which caused the detection of "the error" in the implementation. The error was corrected and the correction was automatically proven correct, again using UPPAAL. A future, and more automated, version of the protocol, where this error is fatal, will incorporate the correction. Hence, this work is an elegant demonstration of how model checking has had an impact on practical software development. The effort of modeling this protocol has in addition generated a number of suggestions for enriching the UPPAAL language. Hence, it's also an excellent example of the reverse impact.
0. This
"... Abstract In this paper we show several results about monotoneplanar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables,compute exactly the functions in nonuniform AC ..."
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Abstract In this paper we show several results about monotoneplanar circuits. We show that monotone planar circuits of bounded width, with access to negated input variables,compute exactly the functions in nonuniform AC
This document in subdirectoryRS/97/32/ HARDNESS RESULTS FOR DYNAMIC PROBLEMS BY EXTENSIONS OF FREDMAN AND SAKS ’ CHRONOGRAM METHOD
, 1997
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
Audio/Video Protocol: An Industrial Case Study Using UPPAAL
, 1997
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
This document in subdirectoryRS/02/50/ Circuits on Cylinders
, 2002
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
A new characterization of ACC⁰ and probabilistic CC⁰
"... ... that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC⁰ circuits. In this work we show that the AND function can be computed by uniform probabilistic CC⁰ circuits that use only O(log n) random bits. This may be ..."
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... that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC⁰ circuits. In this work we show that the AND function can be computed by uniform probabilistic CC⁰ circuits that use only O(log n) random bits. This may be viewed as evidence contrary to the conjecture. As a consequence of our construction we get that all of ACC⁰ can be computed by probabilistic CC⁰ circuits that use only O(log n) random bits. Thus, if one were able to derandomize such circuits, we would obtain a collapse of circuit classes giving ACC⁰ = CC⁰. We present a derandomization of probabilistic CC 0 circuits using AND and OR gates to obtain ACC⁰ = AND ◦ OR ◦ CC⁰ = OR ◦ AND ◦ CC⁰. AND and OR gates of sublinear fanin suffice. Both these results hold for uniform as well as nonuniform circuit classes. For nonuniform circuits we obtain the stronger conclusion that ACC⁰ = rand − ACC⁰ = rand − CC⁰ = rand(log n)−CC⁰, i.e., probabilistic ACC⁰ circuits can be simulated by probabilistic CC⁰ circuits using only O(log n) random bits. As an application of our results we obtain a characterization of ACC⁰ by constant width planar nondeterministic branching programs, improving a previous characterization for the quasipolynomial size setting.
Electronic Colloquium on Computational Complexity, Report No. 130 (2006) Oneinputface MPCVP is Hard for L, but in
"... Abstract. A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed ..."
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Abstract. A monotone planar circuit (MPC) is a Boolean circuit that can be embedded in a plane, and that has only AND and OR gates. Yang showed that the oneinputface monotone planar circuit value problem (MPCVP) is in NC 2, and Limaye et. al. improved the bound to LogCFL. Barrington et. al. showed that evaluating monotone upward stratified circuits, a restricted version of the oneinputface MPCVP, is in LogDCFL. In this paper, we prove that the unrestricted oneinputface MPCVP is also in LogDCFL. We also show this problem to be Lhard under quantifier free projections. Key Words: L, LogDCFL, monotone planar circuits. 1