Abstract
In this paper a measure for the complexity of particular instances with respect to a given decision problem is introduced and investigated. Intuitively, an instance x is considered to be hard for a problem A if every algorithm that decides A and runs "fast" on x needs to look up (a description of) x in a table. A main result states that all problems not in P have infinitely many (polynomially) hard instances. Further, there exist problems in EXPTIME with all their instances being hard. The behavior of hard instances under polynomial reductions and the connections with complexity cores and circuits are studied.
Research of this author was supported in part by NSF grants DCR 83-12472 and DCR-8501226; Current address: Department of Mathematics, University of California, Santa Barbara, CA 93106.
Research of this author was supported by the Academy of Finland.
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© 1986 Springer-Verlag Berlin Heidelberg
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Ko, KI., Orponen, P., Schöning, U., Watanabe, O. (1986). What is a hard instance of a computational problem?. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_99
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DOI: https://doi.org/10.1007/3-540-16486-3_99
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