# Circuit satisfiability and constraint satisfaction around Skolem Arithmetic

@article{Glaer2016CircuitSA, title={Circuit satisfiability and constraint satisfaction around Skolem Arithmetic}, author={Christian Gla{\ss}er and Peter Jonsson and Barnaby Martin}, journal={Theor. Comput. Sci.}, year={2016}, volume={703}, pages={18-36} }

## 6 Citations

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It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity.

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The work shows that the balance problem for { ∖, ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable.

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A survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers is presented, to identify those CSPs that can be solved in polynomial time, and to distinguish them from C SPs that are NP-hard.

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Various NP-hard problems which are in association with VLSI design akin wirelength minimization, area minimization), dead space minimization and so forth are delineated and the significant role of biologically inspired algorithms is discussed in a concise manner.

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This study provides a new paradigm in the field of neural networks by overcoming the overfitting issue and presents an integrated representation of k-satisfiability (kSAT) in a mutation hopfield neural network (MHNN).

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A comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN and provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule.

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