Results 1 
4 of
4
Complexity of twolevel logic minimization
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
"... Abstract—The complexity of twolevel logic minimization is a topic of interest to both computeraided design (CAD) specialists and computer science theoreticians. In the logic synthesis community, twolevel logic minimization forms the foundation for more complex optimization procedures that have si ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
(Show Context)
Abstract—The complexity of twolevel logic minimization is a topic of interest to both computeraided design (CAD) specialists and computer science theoreticians. In the logic synthesis community, twolevel logic minimization forms the foundation for more complex optimization procedures that have significant realworld impact. At the same time, the computational complexity of twolevel logic minimization has posed challenges since the beginning of the field in the 1960s; indeed, some central questions have been resolved only within the last few years, and others remain open. This recent activity has classified some logic optimization problems of high practical relevance, such as finding the minimal sumofproducts (SOP) form and maximal term expansion and reduction. This paper surveys progress in the field with selfcontained expositions of fundamental early results, an account of the recent advances, and some new classifications. It includes an introduction to the relevant concepts and terminology from computational complexity, as well a discussion of the major remaining open problems in the complexity of logic minimization. Index Terms—Computational complexity, logic design, logic minimization, twolevel logic. I.
Complexity of DNF Minimization and Isomorphism Testing for Monotone Formulas
, 2008
"... We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DPc ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DPcomplete to check whether a monomial is a prime implicant for an arbitrary formula, but the equivalent problem for monotone formulas is in L. We show PPcompleteness of checking if the minimum size of a DNF for a monotone formula is at most k, and for k in unary, we show that the complexity of the problem drops to coNP. In [Uma01] a similar problem for arbitrary formulas was shown to be Σ p 2complete. We show that calculating the minimum equivalent DNF for a monotone formula is possible in outputpolynomial time if and only if P = NP. Finally, we disprove a conjecture from [Rei03] by showing that checking whether two formulas are isomorphic has the same complexity for arbitrary formulas as for monotone formulas.
Computing Lower and Upper Bounds on the Probability of Causal Statements
"... Abstract Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraintbased methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typicall ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract Causal discovery provides an opportunity to infer causal relationships from purely observational data and to predict the effect of interventions. Constraintbased methods for causal discovery exploit conditional (in)dependencies to infer the direction of causal relationships. They typically work through forward chaining: given some causal statements, others can be inferred by applying relatively straightforward causal logic such as transitivity and acyclicity. Starting from the premise that we can estimate reliabilities for base causal statements, we propose a novel approach to estimate the reliability of novel statements inferred by forward chaining. Since reliabilities for base statements are clearly dependent, if only because inferred from the same data, exact computation is infeasible. However, lending ideas from the area of imprecise probability theory, we can compute bounds on the reliabilities on inferred statements. Specifically, we make use of the good old Fréchet inequalities and discuss two different variants: greedy and delayed. In simulation experiments, we show that the delayed variant, at the expense of more bookkeeping and computation time, does provide slightly tighter intervals. We illustrate our method on a realworld data set about attention deficit/hyperactivity disorder.
Complexity of DNF Minimization and Isomorphism Testing for Monotone Formulas?
"... We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DP ..."
Abstract
 Add to MetaCart
(Show Context)
We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly from the arbitrary case. We show that it is DPcomplete to check whether a monomial is a prime implicant for an arbitrary formula, but the equivalent problem for monotone formulas is in L. We show PPcompleteness of checking if the minimum size of a DNF for a monotone formula is at most k, and for k in unary, we show that the complexity of the problem drops to coNP. In [Uma01] a similar problem for arbitrary formulas was shown to be Σp2complete. We show that calculating the minimum equivalent DNF for a monotone formula is possible in outputpolynomial time if and only if P = NP. Finally, we disprove a conjecture from [Rei03] by showing that checking whether two formulas are isomorphic has the same complexity for arbitrary formulas as for monotone formulas.