@Article{Devienne_et_al:1996,
AUTHOR = {Devienne, Philippe and Lebegue, Patrick and Parrain, Anne and Routier, JeanChristophe and Würtz, Jörg},
TITLE = {Smallest Horn Clause Programs},
YEAR = {1996},
JOURNAL = {Journal of Logic Programming},
VOLUME = {27},
NUMBER = {3},
PAGES = {227267},
URL = {ftp://ftp.ps.unisb.de/pub/papers/ProgrammingSysLab/JLP96.ps.gz},
ABSTRACT = {The simplest nontrivial program pattern in logic programming is the following one : $$left\beginarrayl p( extitfact)leftarrow\ p( extitleft)leftarrow p( extitright).\ leftarrow p( extitgoal). endarray
ight.defglobble#1gobble$$ where extitfact, extitgoal, extitleft and extitright are arbitrary terms. Because the well known extitappend program matches this pattern, we will denote such programs extitappendlike''. In spite of their simple appearance, we prove in this paper that termination and satisfiability (i.e the existence of answersubstitutions, called the extitemptiness problem) for are undecidable. We also study some subcases depending on the number of occurrences of variables in extitfact, extitgoal, extitleft or extitright. Moreover, we prove that the computational power of extitappendlike programs is equivalent to the one of Turing machines ; we show that there exists an extitappendlike universal program. Thus, we propose an equivalent of the BöhmJacopini theorem for logic programming. This result confirms the expressiveness of logic programming. The proofs are based on program transformations and encoding of problems, unpredictable iterations within number theory defined by J.H. Conway or the Post correspondence problem.},
ANNOTE = {COLIURL : Devienne:1996:SHC.pdf Devienne:1996:SHC.ps} }
