# Algebra, Vol.1 by Redei L.

By Redei L.

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Extra info for Algebra, Vol.1

Sample text

Right now there is only an operational semantics describing this feature but no denotational one. Furthermore, the semantic approaches employed in the area do often lead to lengthy and very technical proofs which often do not convey the central proof idea well, see for instance the proofs in [6]. This is mostly due to the fact that a special aspect called sharing has been abstracted from in high level approaches to program semantics [9]. Adding this aspect in the way proposed in [1] or [8] increases the level of technical detail considerably.

Then, J ∪ N relates two ﬁelds of study if and only if they are diﬀerent and form a combination of the second category. Note that also J and N are symmetric, J is irreﬂexive, and N is reﬂexive. The reﬂexivity of N is motivated by the informal requirement that the duration of study is three years if and only if the two ﬁelds of study of the combination belong to diﬀerent groups of the same block. 1. The relations B : G ↔ G, J : S ↔ S and N : S ↔ S constitute the input of the university timetabling problem.

In: Astesiano, E. ) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 318–321. Springer, Heidelberg (1998) 2. : Implementation of relation algebra using binary decision diagrams. In: de Swart, H. ) RelMiCS 2001. LNCS, vol. 2561, pp. 241–257. Springer, Heidelberg (2002) 3. : RelView – An OBDD-based Computer Algebra system for relations. V. ) CASC 2005. LNCS, vol. 3718, pp. 40–51. Springer, Heidelberg (2005) 4. , Yellen, J. ): Handbook of graph theory. CRC Press, Boca Raton (2003) 5. : Evaluating sets of search points using relational algebra.