The Complexity of Membership Problems for Circuits over Sets of Positive Numbers

@inproceedings{Breunig2007TheCO,
  title={The Complexity of Membership Problems for Circuits over Sets of Positive Numbers},
  author={Hans Georg Breunig},
  booktitle={FCT},
  year={2007}
}
  • H. Breunig
  • Published in FCT 27 August 2007
  • Mathematics
We investigate the problems of testing membership in the subset of the positive numbers produced at the output of (∪∩,-,+,×) combinational circuits. These problems are a natural modification of those studied by McKenzie and Wagner (2003), where circuits computed sets of natural numbers. It turns out that the missing 0 has strong implications, not only because 0 can be used to test for emptiness. We show that the membership problem for the general case and for (∪∩,+,×) is PSPACE-complete… 
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Equivalence Problems for Circuits over Sets of Natural Numbers
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This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪, ∩,-,+, ×}-circuits.
Equivalence Problems for Circuits over Sets of Natural Numbers
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This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪,∩,−,+,×}-circuits.
Emptiness problems for integer circuits
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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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TLDR
The general membership problem for equations of the form Xi=φi (X1,…,Xn) (1≤i≤n) is proved to be EXPTIME-complete, and it is established that least solutions of all such systems are in EXPTime.
Circuit Satisfiability and Constraint Satisfaction Around Skolem Arithmetic
We study interactions between Skolem Arithmetic and certain classes of Circuit Satisfiability and Constraint Satisfaction Problems (CSPs). We revisit results of Glaser et al. [16] in the context of…
Circuit satisfiability and constraint satisfaction around Skolem Arithmetic
Constraint Satisfaction Problems around Skolem Arithmetic
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This work studies interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs) and proves the decidability of SkoleM Arithmetic.
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References

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