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- W2085033370 abstract "Let C be the class of monadic, total monadic or linear monadic recursion schemes. We introduce the executability problem for C and show how its complexity can be used to obtain lower and/or upper bounds on the complexities of decision problems for C . These decision problems include divergence, isomorphism, strong equivalence and weak equivalence. Three possible measures of the maximal possible depths of nesting of function calls in the computations of members of C are also introduced. Lower and upper bounds on these measures are presented in terms of functions of scheme size. Exponential bounds are obtained for the classes of monadic recursion schemes; but polynomial bounds are obtained for the classes of total monadic and linear monadic recursion schemes. One corollary of special interest is the following: There exist c >0 such that a monadic recursion scheme S is total if and only if no computation of S entails a depth of nesting of function calls greater than c · n 2 where n is the size of S . We use these bounds on depths of nesting of function calls to derive a number of nondeterministic polynomially time-bounded or polynomially space-bounded algorithms for decision problems for the classes of schemes C above." @default.
- W2085033370 created "2016-06-24" @default.
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- W2085033370 date "1983-01-01" @default.
- W2085033370 modified "2023-09-23" @default.
- W2085033370 title "The complexity of monadic recursion schemes: Executability problems, nesting depth, and applications" @default.
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- W2085033370 doi "https://doi.org/10.1016/0304-3975(83)90091-9" @default.
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