Balance Problems for Integer Circuits

  title={Balance Problems for Integer Circuits},
  author={Titus Dose},
  booktitle={Electron. Colloquium Comput. Complex.},
  • Titus Dose
  • Published in
    Electron. Colloquium Comput…
    1 December 2019
  • Mathematics, Computer Science
Abstract We investigate the computational complexity of balance problems for { ∖ , ⋅ } -circuits computing finite sets of natural numbers. These problems naturally build on problems for integer expressions and integer circuits studied by Stockmeyer and Meyer (1973), McKenzie and Wagner (2007), and Glaser et al. (2010). Our work shows that the balance problem for { ∖ , ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems… 


Emptiness Problems for Integer Circuits
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.
Equivalence Problems for Circuits over Sets of Natural Numbers
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.
Integer circuit evaluation is PSPACE-complete
  • Ke Yang
  • Mathematics
    Proceedings 15th Annual IEEE Conference on Computational Complexity
  • 2000
The integer circuit problem is PSPACE-complete, resolving an open problem posed by P. McKenzie, H. Vollmer, and K. W. Wagner (2000).
The Complexity of Membership Problems for Circuits over Sets of Positive Numbers
It is shown that the membership problem for the general case and for (∪∩,+,×) is PSPACE-complete, whereas it is NEXPTIME-hard if one allows 0, and several other cases are resolved.
Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers
  • Titus Dose
  • Mathematics, Computer Science
    Electron. Colloquium Comput. Complex.
  • 2016
The computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits, such as L, P, NP, PSPACE, NEXP, and even Sigma_1, the class of c.e. languages, is studied.
Functions Definable by Arithmetic Circuits
Two negative results are proved: the first shows, roughly, that a function is not circuit-definable if it has an infinite range and sub-linear growth; the second shows,roughly, that it has a finite range and fails to converge on certain `sparse' chains under inclusion.
Word problems requiring exponential time(Preliminary Report)
A number of similar decidable word problems from automata theory and logic whose inherent computational complexity can be precisely characterized in terms of time or space requirements on deterministic or nondeterministic Turing machines are considered.
The complexity of theorem-proving procedures
  • S. Cook
  • Mathematics, Computer Science
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a
On the number of integers in a generalized multiplication table
Motivated by the Erdos multiplication table problem we study the following question: Given numbers N_1,...,N_{k+1}, how many distinct products of the form n_1...n_{k+1} with n_i 1. In the present
A survey on counting classes
The authors prove P/sup EP(log)/ 25 PP, investigate the Boolean closure BC( EP) of EP, and give a relativization principle which allows them to completely separate BC(EP) in a suitable relativized world and to give simple proofs for known relativizing results.