We consider the problem of identifying equivalence of two knowledge bases which are capable of abductive reasoning. Here, a knowledge base is written in either first-order logic or nonmonotonic logic programming. In this work, we will give two definitions of abductive equivalence. The first one, explainable equivalence, requires that two abductive programs have the same explainability for any o...

To prove or disprove the computational equivalence of solving the RSA problem and factoring integers is a longstanding open problem in cryptography. This paper provides some evidence towards the validity of this equivalence. We show that any e cient generic ring algorithm which solves the ( exible) low-exponent RSA problem can be converted into an e cient factoring algorithm. Thus, the low-expo...

This study investigated whether activating elements of prior knowledge can influence how problem solvers encode and solve simple mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __). Past work has shown that such problems are difficult for elementary school students (McNeil and Alibali, 2000). One possible reason is that children's experiences in math classes may encourage them to think...

We study the NFA reductions by invariant equivalences. It is well-known that the NFA minimization problem is PSPACE-complete. Therefore, there have been approaches to reduce the size of NFAs in low polynomial time by computing invariant equivalence and merging the states within same equivalence class. Here we consider the nondeterminism reduction of NFAs by invariant equivalences. We, in partic...

It is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. allowing initialized ancilla bits in the input and ignoring “garbage” ancilla bits in the output, is also coNP-complete. The complexity of deciding strong equivalence, including the ancilla bits, is less obvious and may de...

We analyze the technique used by Adams and Kechris (2000) to obtain their results about Borel reducibility of countable Borel equivalence relations. Using this technique, we show that every Σ1 equivalence relation is Borel reducible to the Borel bi-reducibility of countable Borel equivalence relations. We also apply the technique to two other classes of essentially uncountable Borel equivalence...

For an equivalence relation E on the words in some finite alphabet, we consider the recognition problem (decide whether two words are equivalent), the invariant problem (calculate a function constant on precisely the equivalence classes), the normal form problem (calculate a particular member of an equivalence class, given an arbitrary member) and the first member problem (calculate the first m...

one may daresay that the foremost issue and problem in translation is to observe “translation equivalence principle” so that the translated text to be the equivalent and all-out mirror against the original text. to obtain this goal, it is perfectly necessary to pay attention to semantic different layers, ranged from referential meaning to empirical, interactive, implicit, meanings, semantic uni...