Abstract
We propose an information-theoretic approach to proving lower bounds on the size of branching programs (b.p.). The argument is based on Kraft-McMillan type inequalities for the average amount of uncertainty about (or entropy of) a given input during various stages of the computation. We first demonstrate the approach for read-once b.p. Then we introduce a strictly larger class of so-called ‘gentle’ b.p. and, using the suggested approach, prove that some explicit Boolean functions, including the Clique function and a particular Pointer function (which belongs to AC0), cannot be computed by gentle program of polynomial size. These lower bounds are new since explicit functions, which are known to be hard for all previously considered restricted classes of b.p. (like (1, + s)-b.p. or syntactic read-k-times b.p.) can be easily computed by gentle b.p. of polynomial size.
Research supported by the DFG grant Me 1077/10-1.
Research supported by the Grant Agency čR Grant No 201/98/0717 and partly by MšMT čR Grant No. OK-304 and by INCO-Copernicus Contract IP961095 ALTEC-KIT.
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References
Dunne, P. E.: Lower bounds on the complexity of one-time-only branching programs. In: Proc. of FCT'85, Lect. Notes in Comput. Sci., 199 (1985), 90–99.
Jukna, S.: Entropy of contact circuits and lower bounds on their complexity. Theoret. Comput. Sci., 57 (1988), 113–129.
-: A note on read-k-times branching programs. RAIRO Theoretical Informatics and Applications 29:1 (1995), pp. 75–83.
-, Razborov, A. A.: Neither reading few bits twice nor reading illegally helps much. ECCC TR96-037 (1996). To appear in: Discrete Appl. Math.
Neciporuk, E. I.: On a Boolean function. Soviet Mathematics Doklady 7:4 (1966), 999–1000.
Okolnishnikova, E. A.: Lower bounds for branching programs computing characteristic functions of binary codes. Metody discretnogo analiza 51 (1991), pages 61–83.
Wegener, I.: The complexity of Boolean functions, Wiley-Teubner, 1987.
Žák, S.: A sub exponential lower bound for branching programs restricted with regard to some semantic aspects. ECCC TR97-050 (1997).
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© 1998 Springer-Verlag Berlin Heidelberg
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Jukna, S., Žák, S. (1998). On branching programs with bounded uncertainty. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055059
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DOI: https://doi.org/10.1007/BFb0055059
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