A Theory of Cartesian Arrays (with Applications in Quantum Circuit Verification)

Abstract We present a theory of Cartesian arrays, which are multi-dimensional arrays with support for the projection to sub-arrays, as well updating sub-arrays. The resulting logic is an extension Combinatorial Array Logic (CAL) and motivated by analysis quantum circuits: using projection, we can succinctly encode semantics gates quantifier-free formulas verify end-to-end correctness circuits. Since expressive enough represent circuits succinctly, it necessarily has high complexity; show, suffices k -color problem graph under succinct circuit representation, NEXPTIME-complete problem. NEXPTIME decision procedure report on preliminary experiments this procedure.