Ohad Asor

Ohad Asor, Avishy Carmi

Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the integers and is thus a #P problem. Similarly, integrating this function from zero to infinity and deciding whether the result is either zero or infinity is an NP-Complete problem. Efficient numerical integration methods such as the double exponential formula and the sinc approximation have been around since the mid 70's. Noting the hardness of approximating the integral we argue that the proven rates of convergence of such methods cannot possibly be correct since they give rise to an anomalous result as P=#P.

Ohad Asor

We introduce ocLTL, a version of LTL+P modulo ω-categorical theories. We reduce its realizability and synthesis problems into the corresponding problems in propositional LTL+P. The core of the reduction replaces each data subformula with a finite disjunction over complete types. The complexity remains 2-EXPTIME with additional blowup that depends only on the theory but not the formula.

Ohad Asor

Tau-chain is a decentralized peer-to-peer network having three unified faces: Rules, Proofs, and Computer Programs, allowing a generalization of virtually any centralized or decentralized P2P network, together with many new abilities, as we present on this note.