The paper presents a selection of recently developed and/or used techniques for equivalencechecking on infinite-state systems, and an up-to-date overview of existing results (as of September 2004).

We examine the learnability of concepts based on counting functions. A counting function is a generalization of a parity function in which the weighted sum of n inputs is tested for equivalence to some value k modulo N . The concepts we study therefore generalize many commonly studied boolean functions. We first show that disjunctions of counting functions (DOCFs) with modulus N are learnable b...

We prove, in ZF+Σ2-determinacy, that for any analytic equivalence relation E, the following three statements are equivalent: (1) E does not have perfectly many classes, (2) E satisfies hyperarithmetic-is-recursive on a cone, and (3) relative to some oracle, for every equivalence class [Y ]E we have that a real X computes a member of the equivalence class if and only if ω 1 ≥ ω [Y ] 1 . We also ...

A Borel equivalence relation on a Polish space is countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (on the space of subsets of the integers) that occur in recursion theory are: recursive isomorphism, Turing equivalence, arithmetic equivalence, etc. There is a canonical hierarchy of complexity of countable Borel equivalence rel...

aesthetic equivalence is produced when both the source and target texts enjoy the same degree of interpretability with semantic explicitness. this requires both texts to have the same number of indeterminacies. roman ingarden, the polish phenomenologist and aesthetician, was the first one to consider the concept of indeterminacy as a characteristic of literary works. then iser and jauss, two ae...

abstract translation of literary texts, especially poetry, is one of the most difficult tasks; it requires mastery and knowledge of the language system and culture, and lack of this might lead to wrong translation. this study aimed to examine the loss and gain of the sociocultural implicit meanings in the english translations of the mu’allaqat, and assess whether the translators of the mu’allaq...

Definition 1.1. If S is a multiplicative subset of a ring A (commutative with 1), the quotient hyperring A/mS = (A/mS,+, ·,−, 0, 1) is defined as follows: A/mS is the set of equivalence classes with respect to the equivalence relation ∼ on A defined by a ∼ b iff as = bt for some s, t ∈ S. The operations on A/mS are the obvious ones induced by the corresponding operations on A: Denote by a the e...

The first subject we investigate in this thesis deals with optimization problems on graphs. The edges are given costs defined by the values of independent exponential random variables. We show how to calculate some or all moments of the distributions of the costs of some optimization problems on graphs. The second subject that we investigate is 1-error correcting perfect binary codes, perfect c...

Checking the functional equivalence of sequential circuits is an important practical problem. Because general algorithms for solving this problem require a state-space traversal of the product machine, they are computationally expensive. In this paper, we present a new method for sequential equivalence checking which utilizes functionally equivalent signals to prove the equivalence of both circ...