## The complexity of membership problems for circuits over sets of natural numbers (2007)

Citations: | 16 - 0 self |

### BibTeX

@MISC{McKenzie07thecomplexity,

author = {Pierre McKenzie and Klaus W. Wagner},

title = {The complexity of membership problems for circuits over sets of natural numbers},

year = {2007}

}

### Years of Citing Articles

### OpenURL

### Abstract

The problem of testing membership in the subset of the natural numbers produced at the output gate of a {∪, ∩, − , +, ×} combinational circuit is shown to capture a wide range of complexity classes. Although the general problem remains open, the case {∪, ∩, +, ×} is shown NEXPTIME-complete, the cases {∪, ∩, − , ×}, {∪, ∩, ×}, {∪, ∩, +} are shown PSPACE-complete, the case {∪, +} is shown NP-complete, the case {∩, +} is shown C=L-complete, and several other cases are resolved. Interesting auxiliary problems are used, such as testing nonemptyness for union-intersection-concatenation circuits, and expressing each integer, drawn from a set given as input, as powers of relatively prime integers of one’s choosing. Our results extend in nontrivial ways past work by