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 -