Given a ∈ Z \ {±1, 0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerat...

Abstrae%: A framework for the description of syntactic structures of free word order languages is proposed, based on combination of intuitions underlying immediate constituent description, dependency description and communicative dynamism. The combined approach is compared to its sources and shown superior in descriptive power, esp. in the area of free intermixing of (any number of) adjuncts wi...

We introduce refutationally complete superposition calculi for intentional and extensional λ-free higher-order logic, a formalism that allows partial application and applied variables. The intentional variants perfectly coincide with standard superposition on first-order clauses. The calculi are parameterized by a well-founded term order that need not be compatible with arguments, making it pos...

i Conventional distributed adaptive routing strategies usually work well for packet switch ng networks only in the absence of link/node failures. However, they cannot avoid looping messages for an extended period in case of link/node failures. In this paper, we develop a multi-order routing strategy which is loop-free even in the s presence of link/node failures. Unlike most conventional method...

In the last decades, first-order logic (FOL) has become a standard language for describing a large number of mathematical theories. Numerous proof systems for FOL which determine what formulas are universally true emerged over time. On the other hand, higher-order logic (HOL) enables one to describe more theories and to describe existing theories more succinctly. Due to more complicated higher-...

The P r o l o g p r o g r a m m i n g l anguage a l lows the u s e r to w r i t e p o w e r f u l p a r s e r s in the fo rm of m e t a m o r p h o s i s g r a m m a r s . H o w e v e r , the m e t a m o r p h o s i s g r a m m a r s , as de f ined by C o l m e r a u e r 2 , h a v e to s p e c i f y s t r i c t l y the o r d e r of t e r m i n a l and n o n t e r m i n a l s y m b o l s . A m o...

In this paper, I discuss machine translation of English text into a relatively “free” word order language, specifically Turkish. I present algorithms that use contextual information to determine what the topic and the focus of each sentence should be, in order to generate the contextually appropriate word orders in the target language.