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799 results on '"Lingas, Andrzej"'

202. Lower Bounds for DeMorgan Circuits of Bounded Negation Width

Author

Jukna, Stasys, Lingas, Andrzej, Jukna, Stasys, and Lingas, Andrzej

Abstract

We consider Boolean circuits over {or, and, neg} with negations applied only to input variables. To measure the "amount of negation" in such circuits, we introduce the concept of their "negation width". In particular, a circuit computing a monotone Boolean function f(x_1,...,x_n) has negation width w if no nonzero term produced (purely syntactically) by the circuit contains more than w distinct negated variables. Circuits of negation width w=0 are equivalent to monotone Boolean circuits, while those of negation width w=n have no restrictions. Our motivation is that already circuits of moderate negation width w=n^{epsilon} for an arbitrarily small constant epsilon>0 can be even exponentially stronger than monotone circuits. We show that the size of any circuit of negation width w computing f is roughly at least the minimum size of a monotone circuit computing f divided by K=min{w^m,m^w}, where m is the maximum length of a prime implicant of f. We also show that the depth of any circuit of negation width w computing f is roughly at least the minimum depth of a monotone circuit computing f minus log K. Finally, we show that formulas of bounded negation width can be balanced to achieve a logarithmic (in their size) depth without increasing their negation width.

Published
2019
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203. Lower Bounds for DeMorgan Circuits of Bounded Negation Width

Author

Stasys Jukna and Andrzej Lingas, Jukna, Stasys, Lingas, Andrzej, Stasys Jukna and Andrzej Lingas, Jukna, Stasys, and Lingas, Andrzej

Abstract

We consider Boolean circuits over {or, and, neg} with negations applied only to input variables. To measure the "amount of negation" in such circuits, we introduce the concept of their "negation width". In particular, a circuit computing a monotone Boolean function f(x_1,...,x_n) has negation width w if no nonzero term produced (purely syntactically) by the circuit contains more than w distinct negated variables. Circuits of negation width w=0 are equivalent to monotone Boolean circuits, while those of negation width w=n have no restrictions. Our motivation is that already circuits of moderate negation width w=n^{epsilon} for an arbitrarily small constant epsilon>0 can be even exponentially stronger than monotone circuits. We show that the size of any circuit of negation width w computing f is roughly at least the minimum size of a monotone circuit computing f divided by K=min{w^m,m^w}, where m is the maximum length of a prime implicant of f. We also show that the depth of any circuit of negation width w computing f is roughly at least the minimum depth of a monotone circuit computing f minus log K. Finally, we show that formulas of bounded negation width can be balanced to achieve a logarithmic (in their size) depth without increasing their negation width.

Published
2019
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220. Small Normalized Boolean Circuits for Semi-disjoint Bilinear Forms Require Logarithmic Conjunction-depth

Author

Lingas, Andrzej

Subjects
Computer Science::Hardware Architecture, Computer Science::Emerging Technologies, 000 Computer science, knowledge, general works, Computer Science, Hardware_LOGICDESIGN
Abstract

We consider normalized Boolean circuits that use binary operations of disjunction and conjunction, and unary negation, with the restriction that negation can be only applied to input variables. We derive a lower bound trade-off between the size of normalized Boolean circuits computing Boolean semi-disjoint bilinear forms and their conjunction-depth (i.e., the maximum number of and-gates on a directed path to an output gate). In particular, we show that any normalized Boolean circuit of at most epsilon log n conjunction-depth computing the n-dimensional Boolean vector convolution has Omega(n^{2-4 epsilon}) and-gates. Analogously, any normalized Boolean circuit of at most epsilon log n conjunction-depth computing the n x n Boolean matrix product has Omega(n^{3-4 epsilon}) and-gates. We complete our lower-bound trade-offs with upper-bound trade-offs of similar form yielded by the known fast algebraic algorithms.

Published
2018
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224. On a Fire Fighter’s Problem

Author

Klein, Rolf, primary, Langetepe, Elmar, additional, Schwarzwald, Barbara, additional, Levcopoulos, Christos, additional, and Lingas, Andrzej, additional

Published
2019
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229. An optimal expected-time parallel algorithm for Voronoi diagrams

Author

Levcopoulos, Christos, Katajainen, Jyrki, Lingas, Andrzej, Goos, G., editor, Hartmanis, J., editor, Barstow, D., editor, Brauer, W., editor, Brinch Hansen, P., editor, Gries, D., editor, Luckham, D., editor, Moler, C., editor, Pnueli, A., editor, Seegmüller, G., editor, Stoer, J., editor, Wirth, N., editor, Karlsson, Rolf, editor, and Lingas, Andrzej, editor

Published
1988
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230. Small Normalized Boolean Circuits for Semi-disjoint Bilinear Forms Require Logarithmic Conjunction-depth

Author

Andrzej Lingas, Lingas, Andrzej, Andrzej Lingas, and Lingas, Andrzej

Abstract

We consider normalized Boolean circuits that use binary operations of disjunction and conjunction, and unary negation, with the restriction that negation can be only applied to input variables. We derive a lower bound trade-off between the size of normalized Boolean circuits computing Boolean semi-disjoint bilinear forms and their conjunction-depth (i.e., the maximum number of and-gates on a directed path to an output gate). In particular, we show that any normalized Boolean circuit of at most epsilon log n conjunction-depth computing the n-dimensional Boolean vector convolution has Omega(n^{2-4 epsilon}) and-gates. Analogously, any normalized Boolean circuit of at most epsilon log n conjunction-depth computing the n x n Boolean matrix product has Omega(n^{3-4 epsilon}) and-gates. We complete our lower-bound trade-offs with upper-bound trade-offs of similar form yielded by the known fast algebraic algorithms.

Published
2018
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234. Computing the Boolean Product of Two n × n Boolean Matrices Using O(n²) Mechanical Operations.

Author

LINGAS, ANDRZEJ and PERSSON, MIA

Subjects
BOOLEAN matrices, MECHANICAL models, MATRIX multiplications
Abstract

We study the problem of determining the Boolean product of two n × n Boolean matrices in an unconventional computational model allowing for mechanical operations. We show that O(n2) operations are sufficient to compute the product in this model. [ABSTRACT FROM AUTHOR]

Published
2020

242. An O(n log n) algorithm for computing a link center in a simple polygon : Preliminary version

Author

Djidjev, Hristo N., Lingas, Andrzej, Sack, Jörg-Rüdiger, Goos, G., editor, Hartmanis, J., editor, Barstow, D., editor, Brauer, W., editor, Brinch Hansen, P., editor, Gries, D., editor, Luckham, D., editor, Moler, C., editor, Pnueli, A., editor, Seegmüller, G., editor, Stoer, J., editor, Wirth, N., editor, Monien, B., editor, and Cori, R., editor

Published
1989
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245. Subgraph isomorphism for biconnected outerplanar graphs in cubic time

Author

Lingas, Andrzej, Goos, G., editor, Hartmanis, J., editor, Barstow, D., editor, Brauer, W., editor, Brinch Hansen, P., editor, Gries, D., editor, Luckham, D., editor, Moler, C., editor, Pnueli, A., editor, Seegmüller, G., editor, Stoer, J., editor, Wirth, N., editor, Monien, B., editor, and Vidal-Naquet, G., editor

Published
1986
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249. Bounds on the length of convex partitions of polygons

Author

Levcopoulos, Christos, Lingas, Andrzej, Goos, G., editor, Hartmanis, J., editor, Barstow, D., editor, Brauer, W., editor, Brinch Hansen, P., editor, Gries, D., editor, Luckham, D., editor, Moler, C., editor, Pnueli, A., editor, Seegmüller, G., editor, Stoer, J., editor, Wirth, N., editor, Joseph, Mathai, editor, and Shyamasundar, Rudrapatna, editor

Published
1984
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