The complexity of Boolean functions
The complexity of Boolean functions
Minimal polynomials for the conjunction of functions on disjoint variables can be very simple
Information and Computation
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
A very simple function that requires exponential size read-once branching programs
Information Processing Letters
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
Performance Tuning an Algorithm for Compressing Relational Tables
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
A Probabilistic 3-SAT Algorithm Further Improved
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An Improved Exponential-Time Algorithm for k-SAT
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Derandomization of schuler’s algorithm for SAT
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
On the hardness against constant-depth linear-size circuits
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
On the limits of sparsification
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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We study how big the blow-up in size can be when one switches between the CNF and DNF representations of Boolean functions. For a function f : {0, 1}n → {0, 1}, cnfsize(f) denotes the minimum number of clauses in a CNF for f; similarly, dnfsize(f) denotes the minimum number of terms in a DNF for f. For 0 ≤ m ≤ 2n-1, let dnfsize(m, n) be the maximum dnfsize(f) for a function f : {0, 1}n → {0, 1} with cnfsize(f) ≤ m. We show that there are constants c1, c2 ≥ 1 and ε 0, such that for all large n and all m ∈ [ 1/ε n, 2εn], we have 2n-c1(n/log(m/n)) ≤ dnfsize(m, n) ≤ 2n-c2(n/log(m/n)). In particular, when m is the polynomial nc, we get dnfsize(nc, n) = 2n-θ(c-1(n/log n)).