Satisfiability of the smallest binary program

Philipp Hanschke, Jörg Würtz
1993 Information Processing Letters  
The DFKI conducts application-oriented basic research in the field of artificial intelligence and other related subfields of computer science. The overall goal is to construct systems with technical knowledge and common sense which -by using AI methods -implement a problem solution for a selected application area. Currently, there are the following research areas at the DFKI: Intelligent Engineering Systems Intelligent User Interfaces Computer Linguistics Programming Systems Deduction and
more » ... gent Systems Document Analysis and Office Automation. The DFKI strives at making its research results available to the scientific community. There exist many contacts to domestic and foreign research institutions, both in academy and industry. The DFKI hosts technology transfer workshops for shareholders and other interested groups in order to inform about the current state of research. From its beginning, the DFKI has provided an attractive working environment for AI researchers from Germany and from all over the world. The goal is to have a staff of about 100 researchers at the end of the building-up phase. Abstract Recursivity i s w ell known to be a crucial and important concept in programming theory. The simplest scheme of recursion in the context of logic programming is the binary Horn clause P (l 1 : : : l n ) P (r 1 : : : r n ) . The decidability of the satis ability problem of programs consisting of such a rule, a fact and a goal { called smallest binary program { has been a goal of research for some time. In this paper the undecidability of the smallest binary program is shown by a simple reduction of the Post Correspondence Problem.
doi:10.1016/0020-0190(93)90210-z fatcat:kny57wvv4neqnihzadtwysb6ei