Abstract
Different versions of vector languages are introduced as input languages for the succinct description of instances to combinatorial problems. For some of these languages we prove: (1) These languages are hard input languages, i.e. all popular non-trivial combinatorial problems have the maximum complexity blow-up if the instances are described by the language and (2) These languages are simpler than (i.e. there are simple compilers to) all other hard input languages investigated so far. To prove (1) we introduce different versions of vector-reducibilities which are restricted AC0 reducibilities. This investigation gives partial answers to the questions: How simple can hard instances to a combinatorial problem be ? How simple can the reductions between the most popular combinatorial problems be
(Extended Abstract)
This work has been supported by Deutsche Forschungsgemeinschaft DFG Grant WA 594/1-1.
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© 1990 Springer-Verlag Berlin Heidelberg
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Kowaluk, M., Wagner, K.W. (1990). Vector language: Simple description of hard instances. In: Rovan, B. (eds) Mathematical Foundations of Computer Science 1990. MFCS 1990. Lecture Notes in Computer Science, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029632
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DOI: https://doi.org/10.1007/BFb0029632
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