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- research-articleJuly 2020
Hardness Characterisations and Size-Width Lower Bounds for QBF Resolution
LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer SciencePages 209–223https://doi.org/10.1145/3373718.3394793We provide a tight characterisation of proof size in resolution for quantified Boolean formulas (QBF) by circuit complexity. Such a characterisation was previously obtained for a hierarchy of QBF Frege systems (Beyersdorff & Pich, LICS 2016), but ...
- research-articleSeptember 2019
New Insights on the (Non-)Hardness of Circuit Minimization and Related Problems
ACM Transactions on Computation Theory (TOCT), Volume 11, Issue 4Article No.: 27, Pages 1–27https://doi.org/10.1145/3349616The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deal with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We show that, under very modest cryptographic assumptions (such as the existence ...
- ArticleApril 2010
The size and depth of layered boolean circuits
LATIN'10: Proceedings of the 9th Latin American conference on Theoretical InformaticsPages 372–383https://doi.org/10.1007/978-3-642-12200-2_33We consider the relationship between size and depth for layered Boolean circuits, synchronous circuits and planar circuits as well as classes of circuits with small separators. In particular, we show that every layered Boolean circuit of size s can be ...
- articleNovember 2005
On converting CNF to DNF
Theoretical Computer Science (TCSC), Volume 347, Issue 1-2Pages 325–335https://doi.org/10.1016/j.tcs.2005.07.029We study how big the blow-up in size can be when one switches between the CNF and DNF representations of Boolean functions. For a function f : {0, 1}n → {0, 1}, cnfsize(f) denotes the minimum number of clauses in a CNF for f; similarly, dnfsize(f) ...
- ArticleDecember 2000
Is IDDQ testing not applicable for deep submicron VLSI in year 2011?
In this work, IDDQ current for deep submicron VLSI in year 2011 is estimated with a statistical approach according to the International Technology Roadmap for Semiconductors 1999 Edition considering process variations and different input vectors. The ...
- ArticleMarch 1995
Quasi-algebraic decompositions of switching functions
Brayton (1982-90) and others have developed a rich theory of decomposition of switching functions based on algebraic manipulations of monomials. In this theory, a product g(X/sub g/)/spl middot/h(X/sub h/) is algebraic if X/sub g//spl cap/X/sub h/=O. ...
- research-articleSeptember 1977
A $2.5n$-Lower Bound on the Combinational Complexity of Boolean Functions
Consider the combinational complexity $L(f)$ of Boolean functions over the basis $\Omega = \{ f|f:\{ 0,1\} ^2 \to \{ 0,1\} \} $. A new method for proving linear lower bounds of size $2n$ is presented. Combining it with methods presented in Savage [13, (...