The fundamental difference between depth and delay
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V. M. Khrapchenko
Abstract
Earlier, it was proved that even for a minimal circuit the delay T could be much less than the depth D. Namely, an infinite sequence of minimal circuits was constructed such that T < log2D + 6 and D → ∞. This result would be more interesting if the inequality were true for all equivalent minimal circuits. In this paper, we present an infinite sequence of Boolean functions Fk, k = 1, 2,…, such that any minimal circuit for an arbitrary function Fk has the depth and the delay obeying the inequality T < log2D + 14.
This research was supported by the Program of Basic Research of Department of Applied Mathematics of Russian Academy of Sciences ‘Algebraic and Combinatorial Methods of Mathematical Cybernetics,’ project ‘Design and Complexity of Control Systems.’
© de Gruyter 2008
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- Finite probabilistic structures
- Consistency and an algorithm recognising inconsistency of realisations of a system of random discrete equations with two-valued unknowns
- A simple upper bound for the number of spanning trees of regular graphs
- Dynamic databases with optimal in order time complexity
- The closure operator with the equality predicate branching on the set of partial Boolean functions
- The fundamental difference between depth and delay
- Homomorphisms of shift registers into linear automata
- Provable security of digital signatures in the tamper-proof device model
- Local factorisations of nonlocal Fitting classes
Articles in the same Issue
- Finite probabilistic structures
- Consistency and an algorithm recognising inconsistency of realisations of a system of random discrete equations with two-valued unknowns
- A simple upper bound for the number of spanning trees of regular graphs
- Dynamic databases with optimal in order time complexity
- The closure operator with the equality predicate branching on the set of partial Boolean functions
- The fundamental difference between depth and delay
- Homomorphisms of shift registers into linear automata
- Provable security of digital signatures in the tamper-proof device model
- Local factorisations of nonlocal Fitting classes
