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WS 2011-2012 09.01.2012 Exercises to the Lecture FSVT

Prof. Dr. Klaus Madlener sheet 11

Exercise 1:

Letsig = ({int},0 :→int, s, abs:int→int,+,−:int, int→int).

Prove that there is no finite specification for thesig-algebra Z with the usual interpre- tation of 0, s,+,−,and abs. I.e. there is no finite sig- specification specs.t.Tspec∼=Z.

Exercise 2:

Prove theorem 10.15.: For every recursive term-generatedsig-algebraA, there is a finite enrichment sig0 of sig and a finite specificationspec0 = (sig0, E) withTspec0 |sig ∼=A.

Delivery: until 16.01.2012,

by E-Mail to huechting@informatik.uni-kl.de

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