TY - GEN

T1 - Complexity of counting output patterns of logic circuits

AU - Uchizawa, Kei

AU - Wang, Zhenghong

AU - Morizumi, Hiroki

AU - Zhou, Xiao

PY - 2013

Y1 - 2013

N2 - Let C be a logic circuit consisting of s gates g1, g2, gs, then the output pattern of C for an input x ε {0, 1}n is defined to be a vector (g1(x), g2(x), gs(x)) ε {0, 1}s of the outputs of g1, g2, gs for x. For each f : {0, 1}2 → {0, 1}, we define an f-circuit as a logic circuit where every gate computes f, and investigate computational complexity of the following counting problem: Given an f-circuit C, how many output patterns arise in C? We then provide a dichotomy result on the counting problem: We prove that the problem is solvable in polynomial time if f is PARITY or any degenerate function, while the problem is #P-complete even for constant-depth f-circuits if f is one of the other functions, such as AND, OR, NAND and NOR.

AB - Let C be a logic circuit consisting of s gates g1, g2, gs, then the output pattern of C for an input x ε {0, 1}n is defined to be a vector (g1(x), g2(x), gs(x)) ε {0, 1}s of the outputs of g1, g2, gs for x. For each f : {0, 1}2 → {0, 1}, we define an f-circuit as a logic circuit where every gate computes f, and investigate computational complexity of the following counting problem: Given an f-circuit C, how many output patterns arise in C? We then provide a dichotomy result on the counting problem: We prove that the problem is solvable in polynomial time if f is PARITY or any degenerate function, while the problem is #P-complete even for constant-depth f-circuits if f is one of the other functions, such as AND, OR, NAND and NOR.

KW - Boolean functions

KW - Counting complexity

KW - Logic circuits

KW - Minimum AND-circuits problem

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M3 - Conference contribution

AN - SCOPUS:84925965341

SN - 9781921770265

T3 - Conferences in Research and Practice in Information Technology Series

SP - 37

EP - 42

BT - Conferences in Research and Practice in Information Technology Series

A2 - Wirth, Anthony

PB - Australian Computer Society

T2 - Computing: The Australasian Theory Symposium, CATS 2013

Y2 - 29 January 2013 through 1 February 2013

ER -