Classification problems have been introduced by M. Ziegler as a generalization of promise problems. In this paper we are concerned with solvability and unsolvability questions with respect to a given set or language family, especially with cores of unsolvability. We generalize the results about unsolvability cores in promise problems to classification problems. Our main results are a characteri...

We describe our effort to evaluate the syntax and constraints of Promise Theory using a tool developed in theMaude framework. Through the development of a Maude module we are able to do searches and queries in all possible syntactically valid Promise expressions of an arbitrary initial state of participants and constraints. We use this approach to improve the set of grammatical rules that is al...

This article documents two programmatic comments regarding testing graph properties, which I made during the Dagstuhl workshop on Sublinear-Time Algorithms (July 2005). The first comment advocates paying more attention to the dependence of the tester’s complexity on the proximity parameter. The second comment advocates paying more attention to the question of testing general graphs (rather than...

We consider the following (promise) problem, denoted ED (for Entropy Difference): The input is a pair of circuits, and YES instances (resp., NO instances) are such pairs in which the first (resp., second) circuit generates a distribution with noticeably higher entropy. On one hand we show that any language having a (honest-verifier) statistical zero-knowledge proof is Karpreducible to ED. On th...

We consider the problems of deciding whether the joint distribution sampled by a given circuit satisfies certain statistical properties such as being i.i.d., being exchangeable, being pairwise independent, having two coordinates with identical marginals, having two uncorrelated coordinates, and many other variants. We give a proof that simultaneously shows all these problems are C = P-complete,...

Promise theory defines a method by which static service bindings are made in a network, but little work has been done on handling the dynamic case in which bindings must change over time due to both contingencies and changes in policy. We define two new kinds of promises that provide temporal scope for a conditional promise. We show that simple temporally-scoped promises can describe common net...

We consider an instance of the following problem: Parties P1, . . . , Pk each receive an input xi, and a coordinator (distinct from each of these parties) wishes to compute f(x1, . . . , xk) for some predicate f . We are interested in one-round protocols where each party sends a single message to the coordinator; there is no communication between the parties themselves. What is the minimum comm...

The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance h between two strings of length n is greater than a or less than b, where the gap g = |a − b| ≥ 1 and a and b could depend on n. In this short note, we give a lower bound of Ω( √ n/g) on the quantum query complexity of computing the GapHamming distance between two given strings of lenght n. The proof is ...

The framework of promise theory offers an alternative way of understanding programming models, especially in distributed systems. We show that promise theory can express some familiar constructs and resolve some problems in program interface design, using fewer and simpler concepts than the Unified Modelling Language (UML).

Using Promise Theory as a calculus, I review how to define agency in a scalable way, for the purpose of understanding semantic spacetimes. By following simple scaling rules, replacing individual agents with ‘super-agents’ (sub-spaces), it is shown how agency can be scaled both dynamically and semantically. The notion of occupancy and tenancy, or how space is used and filled in different ways, i...