Size-time complexity of Boolean networks for prefix computations

Program Size Complexity for Possibly Infinite Computations

We define a program size complexity function H∞ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in {0, 1} relative to the H∞ complexity. We prove that the classes of Martin-Löf random sequences and H∞-random sequences coincide, and that the H∞-tr...

Exponential Complexity of Satisfiability Testing for Linear-Size Boolean Formulas

The exponential complexity of the satisfiability problem for a given class of Boolean circuits is defined to be the infimum of constants α such that the problem can be solved in time poly(m) 2, where m is the circuit size and n is the number of input variables [IP01]. We consider satisfiability of linear Boolean formula over the full binary basis and we show that the corresponding exponential c...

Prefix Computations on Symmetric Multiprocessors

We introduce a new prefix computation algorithm on linked lists which builds upon the sparse ruling set approach of Reid-Miller and Blelloch. Besides being somewhat simpler and requiring nearly half the number of memory accesses, we can bound our complexity with high probability instead of merely on average. Moreover, whereas Reid-Miller and Blelloch targeted their algorithm for implementation ...

The Complexity of Computations by Networks

Complexity Results for Prefix Grammars

Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE. We also show that membership for these grammars is complete in P (it was known that this problem is in P) and characterize the complexity of equivalence and inclusion for monotonic grammars. For grammars with several premises we show that membership is complete in EXPTIME and hard...