arXiv subjects

Ohad Asor

Publications and source records attributed to Ohad Asor.

5 recordsLinked to original sources

arXiv2026

ocLTL: LTL Realizability and Synthesis Modulo {\omega}-Categorical Structures

We introduce ocLTL, the case of LTL+P modulo {\omega}-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 an additional blowup that depends only on the theory but not the formula. We demonstrate an application of this framework that is related to atomless Boolean algebras and Lindenbaum-Tarski algebras while drawing a connection to AI safety.

cs.LO↗

arXiv2024

Guarded Successor: A Novel Temporal Logic

We present GS (Guarded Successor), a novel decidable temporal logic with several unique distinctive features. Among those, it allows infinitely many data values that come not only with equality but with a somehow rich theory too: the first-order theory of atomless Boolean algebras. The language also distinguishes between inputs and outputs, and has a decision procedure for determining whether for all inputs exist outputs, at each point of time. Moreover, and maybe most surprisingly, the data values can be nothing but sentences in GS itself. We also present a non-temporal fragment called NSO (Nullary Second Order) that enjoys merely this last property. These results are crucial necessary ingredients in any meaningful design of safe AI. Finally, all those results are obtained from a novel treatment of the first-order theory of atomless Boolean algebras.

cs.LO↗

arXiv2016

Spectral and Modular Analysis of #P Problems

We present various analytic and number theoretic results concerning the #SAT problem as reflected when reduced into a #PART problem. As an application we propose a heuristic to probabilistically estimate the solution of #SAT problems.

cs.CC↗

arXiv2015

On Approximating Univariate NP-Hard Integrals

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.

math.NA↗

arXiv2015

About Tau-Chain

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.

cs.AI↗