Algebraic Methodology and Software Technology (AMAST’93): by Maurice Nivat, Charles Rattray BSc, MSc, FIMA, FBCS, C.Eng., PDF

By Maurice Nivat, Charles Rattray BSc, MSc, FIMA, FBCS, C.Eng., C.Math., Teodor Rus PhD (auth.), Maurice Nivat, Charles Rattray BSc, MSc, FIMA, FBCS, C.Eng., C.Math., Teodor Rus PhD, Giuseppe Scollo PhD (eds.)

ISBN-10: 1447132270

ISBN-13: 9781447132271

ISBN-10: 3540198520

ISBN-13: 9783540198529

The objective of the AMAST meetings is to foster algebraic technique as a origin for software program know-how, and to teach that this may bring about sensible mathematical possible choices to the ad-hoc techniques universal in software program engineering and improvement. the 1st AMAST meetings, held in may possibly 1989 and will 1991 on the college of Iowa, have been good obtained and inspired the ordinary association of additional AMAST meetings on a biennial time table. The 3rd convention on Algebraic technique and software program expertise was once held within the campus of the collage of Twente, The Netherlands, throughout the first week of summer season 1993. approximately 100 humans from all continents attended the convention. the most important curiosity bought by means of the AMAST convention one of the pros prolonged to incorporate the management firms to boot. AMAST'93 used to be opened by means of the Rector of the college of Twente, by means of the neighborhood Chairman. Their establishing addresses open this complaints, too. The court cases includes eight invited papers and 32 chosen communica­ tions. the choice used to be very strict, for 121 submissions have been received.

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Extra resources for Algebraic Methodology and Software Technology (AMAST’93): Proceedings of the Third International Conference on Algebraic Methodology and Software Technology, University of Twente, Enschede, The Netherlands 21–25 June 1993

Example text

There are many other equivalent axiomatizations for relation algebras. For example, equations (ix)-(xiii) can be replaced with the cycle law or with Theorem K. Also, equations (i)-(vi) can be replaced with some other set of equations that define Boolean algebras. The algebra containing all binary relations on the universe U is denoted 9U(U). Identities (i)-(xv) hold in 9U(U), so 9U(U) is a relation algebra. Relation algebras are defined by equations, so it follows that subalgebras, homomorphic images, and direct products of relation algebras are again relation algebras.

Compass Algebras Let the universe be the set of all points in the n-dimensional Euclidean space R n, where R is the set of real numbers. Let R+ be the set of positive real numbers. For every vector v in R n define two binary relations on R n as follows: ={{x,y}: x,y ERn and for some r in R+, x + rv =y}, Ev = {{x,y}: x,y ERn and for some in R, x+ = y}. Dv T Here are some easily proved properties of these relations. TV 32 l' m m m p p pdoms m p pdoml p d d dol 0 p p p d08 d08 0 dol p m p m I'll 1'S8 s p 8 dol I m I dOB m FIGURE p m m P s s 8 p p 8 p pdoml d pdoml d dol 0 dol porn dol m m dol s l's8 d p 0 I I pdorns I I p p d JOB dos 0 dos pdoms d m m d 0 I I'll pom d I'll l's8 8 porn d p porn dOB p I 2.

Theorem 5. Let 2l be a relation algebra witb nonzero elements x, y, z sucb tbat (i) 1', x, x, y, Y, z, z are pairwise disjoint, (ii)y·x;x=O, (iii) y. x;y = 0, (iv) y . y;x = 0, (v) y. y;z = 0, (vi) y. z;y = 0, (vii) y. z;z = 0, (viii) x· z;x = 0, (ix) x· x;z = 0, (x) z ~ z;z, z ~ z;z, z ~ z;z, (xi) y ~ y;y, y ~ y;Y, y ~ Y;y, (xii) y ~ x;z, x ~ ViZ, z ~ x;y, (xiii) y ~ z;x, z ~ y;x, x ~ z;y, (xiv) z ~ z;y, z ~ z;y, y ~ z;z, (xv) z ~ ViZ, Y ~ z;z, z ~ Y;z, (xvi) z ~ z;x, z ~ z;x, x ~ z;z, (xvii) z ~ x;z, x ~ z;z, z ~ x;z, (xviii) l' ~ x;x· x;x· y;Y' Y;y· z;z· z;z.

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Algebraic Methodology and Software Technology (AMAST’93): Proceedings of the Third International Conference on Algebraic Methodology and Software Technology, University of Twente, Enschede, The Netherlands 21–25 June 1993 by Maurice Nivat, Charles Rattray BSc, MSc, FIMA, FBCS, C.Eng., C.Math., Teodor Rus PhD (auth.), Maurice Nivat, Charles Rattray BSc, MSc, FIMA, FBCS, C.Eng., C.Math., Teodor Rus PhD, Giuseppe Scollo PhD (eds.)


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