TY - JOUR
T1 - On distributions computable by random walks on graphs
AU - Kindler, Guy
AU - Romik, Dan
PY - 2004/4
Y1 - 2004/4
N2 - We answer a question raised by Donald E. Knuth and Andrew C. Yao, concerning the class of polynomials on [0,1] that can be realized as the distribution function of a random variable, whose binary expansion is the output of a finite state automaton driven by unbiased coin tosses. The polynomial distribution functions which can be obtained in this way are precisely those with rational coefficients, whose derivative has no irrational roots on [0,1]. We also show, strengthening a result of Knuth and Yao, that all smooth distribution functions which can be obtained by such automata are polynomials.
AB - We answer a question raised by Donald E. Knuth and Andrew C. Yao, concerning the class of polynomials on [0,1] that can be realized as the distribution function of a random variable, whose binary expansion is the output of a finite state automaton driven by unbiased coin tosses. The polynomial distribution functions which can be obtained in this way are precisely those with rational coefficients, whose derivative has no irrational roots on [0,1]. We also show, strengthening a result of Knuth and Yao, that all smooth distribution functions which can be obtained by such automata are polynomials.
KW - Automata
KW - Finite-state generator
KW - Random number generation
KW - Random walks on graphs
UR - http://www.scopus.com/inward/record.url?scp=9744248285&partnerID=8YFLogxK
U2 - 10.1137/S089548010343106X
DO - 10.1137/S089548010343106X
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AN - SCOPUS:9744248285
SN - 0895-4801
VL - 17
SP - 624
EP - 633
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 4
ER -