April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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Tractable and Non-tractable Problems 489
17.12 EVEN HARDER PROBLEMS
There are some problems which are harder than the EXPTIME problems. For example, if we try to specify
propositions using usual mathematical language, that is, using operations like add, sub, mul, div, relations
like >, <, and sets of objects, existence and universality of objects, then effi cient methods for determination
of the truth values are not available. Some of them have complexity of 2
2
n
, that is, doubly exponential. Some
have a complexity which is a Tower function, t (k) that we have seen earlier.
One well-known formalism called Presburger Arithmetic has such a double-exponential time
complexity. It allows us to talk about positive integers, variables which take such ...
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