Nondeterminism and An Abstract Formulation of Nečiporuk’s Lower Bound Method

A formulation of Nečiporuk’s lower bound method slightly more inclusive than the usual complexity-measure-specific formulation is presented. Using this general formulation, limitations to lower bounds achievable by the method are obtained for several computation models, such as branching programs and Boolean formulas having access to a sublinear number of nondeterministic bits. In particular, it is shown that any lower bound achievable by the method of Nečiporuk for the size of nondeterministic and parity branching programs is at most O(n3/2/logn).

[1]  Alexander A. Razborov,et al.  Lower Bounds for Deterministic and Nondeterministic Branching Programs , 1991, FCT.

[2]  Stasys Jukna,et al.  Boolean Function Complexity Advances and Frontiers , 2012, Bull. EATCS.

[3]  Johan Hå stad.  The Shrinkage Exponent of de Morgan Formulas is 2 , 1998 .

[4]  Noga Alon,et al.  On Neciporuk's Theorem for Branching Programs , 1989, Theor. Comput. Sci..

[5]  Stasys Jukna,et al.  Extremal Combinatorics - With Applications in Computer Science , 2001, Texts in Theoretical Computer Science. An EATCS Series.

[6]  Alan Cobham,et al.  The Recognition Problem for the Set of Perfect Squares , 1966, SWAT.

[7]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[8]  Juraj Hromkovic,et al.  Nondeterministic communication with a limited number of advice bits , 1996, STOC '96.

[9]  C. Papadimitriou,et al.  The Complexity of Computing a , 2009 .

[10]  Johan Håstad.  The Shrinkage Exponent of de Morgan Formulas is 2 , 1998, SIAM J. Comput..

[11]  Alois Potton.  Komplexitätstheorie , 1995, PIK Prax. Informationsverarbeitung Kommun..

[12]  Judy Goldsmith,et al.  Limited nondeterminism , 1996, SIGA.

[13]  Hartmut Klauck,et al.  One-way communication complexity and the Neciporuk lower bound on formula size , 2001, SIAM J. Comput..

[14]  Avi Wigderson,et al.  On span programs , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[15]  I. Wegener.  Branching Programs and Binary Deci-sion Diagrams-Theory and Applications , 1987 .

[16]  Ingo Wegener,et al.  The Complexity of Symmetric Boolean Functions , 1987, Computation Theory and Logic.

[17]  Ravi B. Boppana,et al.  The Complexity of Finite Functions , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[18]  William Joseph Masek,et al.  A fast algorithm for the string editing problem and decision graph complexity , 1976 .

[19]  Pavel Pudlák.  The hierarchy of Boolean circuits , 1987 .