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LISP ProgramSize Complexity
, 1992
"... A theory of programsize complexity for something close to real LISP is sketched. 1 This paper should be called "On the length of programs for computing finite binary sequences in LISP," since it closely follows references [3] to [6]. But that's too long! Copyright c fl 1992, Elsevie ..."
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Cited by 5 (3 self)
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A theory of programsize complexity for something close to real LISP is sketched. 1 This paper should be called "On the length of programs for computing finite binary sequences in LISP," since it closely follows references [3] to [6]. But that's too long! Copyright c fl 1992
LISP ProgramSize Complexity III
 Applied Mathematics and Computation
, 1992
"... We present a "parenthesisfree" dialect of LISP, in which (a) each primitive function has a fixed number of arguments, and (b) the parentheses associating a primitive function with its arguments are implicit and are omitted. The parenthesisfree complexity of an Sexpression e is defined t ..."
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Cited by 1 (1 self)
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to be the minimum size in characters p of a parenthesisfree LISP expression p that has the value e. We develop a theory of programsize complexity for parenthesisfree LISP by showing (a) that the maximum possible parenthesisfree complexity of an nbit string is #n,and(b) how to construct three
Lisp ProgramSize Complexity II
, 1992
"... We present the informationtheoretic incompleteness theorems that arise in a theory of programsize complexity based on something close to real LISP. The complexity of a formal axiomatic system is defined to be the minimum size in characters of a LISP definition of the proofchecking function associa ..."
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Cited by 1 (1 self)
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We present the informationtheoretic incompleteness theorems that arise in a theory of programsize complexity based on something close to real LISP. The complexity of a formal axiomatic system is defined to be the minimum size in characters of a LISP definition of the proofchecking function
The programsize complexity of selfassembled squares
 In Proceedings of the thirtysecond annual ACM symposium on Theory of computing
, 2000
"... ..."
Program Size Complexity for Possibly Infinite Computations
"... We define a program size complexity function H # as a variant of the prefixfree Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in relative to the H # complexity. We prove ..."
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Cited by 2 (0 self)
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We define a program size complexity function H # as a variant of the prefixfree Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in relative to the H # complexity. We
Program size complexity for possibly infinite computations
"... We define a program size complexity function H ∞ as a variant of the prefixfree Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in {0, 1} ω relative to the H ∞ complexity. We prove ..."
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We define a program size complexity function H ∞ as a variant of the prefixfree Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in {0, 1} ω relative to the H ∞ complexity. We
A ProgramSize Complexity Measure for Mathematical Problems and Conjectures
, 2012
"... Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way, w ..."
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Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way
A Theory of Program Size Formally Identical to Information Theory
, 1975
"... A new definition of programsize complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest selfdelimiting program for calculating strings A and B if one is given a minimalsize selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1) ..."
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Cited by 380 (15 self)
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A new definition of programsize complexity is made. H(A;B=C;D) is defined to be the size in bits of the shortest selfdelimiting program for calculating strings A and B if one is given a minimalsize selfdelimiting program for calculating strings C and D. This differs from previous definitions: (1
Results 1  10
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2,768