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Parsimony Hierarchies for Inductive Inference - Ambainis, Case, Jain, Suraj (Correct)
....In Section 1.1 are informally presented what we need of the basic concepts and motivations from inductive inference including parsimony constraints on inferred (learned) programs. As we will see, degrees of parsimony will be measured with notations from Kleene s O for the constructive ordinals [Rog67] Section 1.2 presents a corresponding informal introduction with motivations and examples. Section 1.3 summarizes our principal results. These feature infinite hierarchies of success criteria re inferring parsimonious programs, and they are based on O measured degrees of parsimony. Section 2 ....
....compute f(x) and decode) The trial and error aspect of algorithmically learning such explanatory programs p models that the scientific community changes its mind over time as to explanations for a phenomenon. Informally, acceptable programming systems (synonym: acceptable numberings) Rog58, Rog67, MY78, Roy87] are those programming systems for the partial computable functions which are intercompilable with naturally occurring general purpose programming formalisms such as Turing machine formalisms and the LISP programming language. The programs output by inductive inference algorithms ....
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H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw Hill, New York, 1967. Reprinted, MIT Press, 1987.
Generality's Price: - Inescapable Deficiencies In (Correct)
....j. By convention, x, y, range over finite sequences of numbers, the length of which will always be clear from context. We will freely pun between x 2 N as a number and a 0 1 string. Let h Delta; Deltai be a standard, poly time computable pairing function, e.g. the one from Rogers [Rog67]. By convention, for each n 2 and each x 1 ; xn 1 2 N, we recursively define hx 1 ; xn 1 i = def hx 1 ; hx 2 ; xn 1 ii. Encoding lists. For each x; y 2 N, let x Pi y denote the concatenation of (the dyadic representations of) x and y. For each x 2 N, let E(x) 1 jxj 0 ....
....less; and f = g means g 2 FV(f ) Programming systems. We say that a partial recursive : N N is a programming system for a class of functions S PR if and only if S = f x (i; x) i 2 N g. We typically write i (x) for (i; x) We say that is an acceptable programming system of S [Rog67,RC94] if and only if it is the case that for any other programming system for S, say , there is a recursive function t such that, for all i, t(i) i , that is, there is an effective way of translating (or reducing) programs into equivalent programs. Let be an acceptable programming system ....
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H. Rogers, Theory of recursive functions and effective computability, McGraw Hill, New York,
Structural Operational Semantics - Aceto, Fokkink, Verhoef (1999) (15 citations) (Correct)
....The trigger of ae is the tuple (l 1 ; l ar(f) with l i = a i if i 2 I and l i = otherwise. We say that a signature Sigma is decidable if there is an algorithm that answers yes if the input is the encoding of a function symbol in Sigma, and no for all other inputs (see, e.g. [186]) The following classification of De Simone languages, and the subsequent result, stem from [101] Definition 5.14 (Properties of De Simone languages) A De Simone language over a signature Sigma is: ffl recursively enumerable if Sigma is decidable and the set of De Simone rules is recursively ....
H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill Book Co., 1967.
... Afmc - Kupferman, Vardi (Correct)
....in computer science, even strict ones, it is possible to show local coalescence, where membership in some class of the hierarchy and in its complementary class implies membership in a lower class. For example, RE co RE = Rec describes coalescence at the bottom of the arithmetical hierarchy [Rog67]. On the other hand, the analogous coalescence for the polynomial hierarchy is not known; it is a major open question whether NP co NP = P [GJ79] In [KV01] we showed that the bottom levels of the calculus expressiveness hierarchy coalesce: 1 1 ML. In other words, if we can express a ....
H. Rogers, Theory of recursive functions and effective computability. McGraw-Hill, 1967.
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....h(r (y) is defined, we have h(r (y) h(r(f(y) r(h (f(y) r (g(h (f(y) Hence, g oh of is a r simulator of h. Similarly, r(r (y) r(r(f(y) F(f(Y) so that r of is a r simulator of r. Example 3.1. Let (N; 0, succ; G K , where K is the halting set of some G6del numbering [29], and let Y= N;0, succ; Then it cannot be the case that errS, For if ,r, then Y by Theorem 3.1, and thus by Theorem 3.2, where t is the identity mapping. But this conclusion contradicts the undecidability of K. This example indicates that our simulation definitions are strong ....
H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.
Dynamic Logic - Harel, Kozen, Tiuryn (1984) (356 citations) (Correct)
.... 1977] Dynamic Logic, which emphasizes the modal nature of the program assertion interaction, was introduced by [Pratt, 1976] Background material on mathematical logic, computability, formal languages and automata, and program verification can be found in [Shoenfield, 1967] logic) [Rogers, 1967] (recursion theory) Kozen, 1997a] formal languages, automata, and computability) Keisler, 1971] infinitary logic) Manna, 1974] program verification) and [Harel, 1992; Lewis and Papadimitriou, 1981; Davis et al. 1994] computability and complexity) Much of this introductory material as ....
H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967.
A Constraint-based Partial Evaluator for Functional - Logic Programs And (Correct)
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H. Rogers. Theory of recursive functions and effective computability. McGraw-Hill, 1967.
A Transformation Framework for Solving Artificial Life Systems .. - GopalaKrishna (2005) (Correct)
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Rogers, J. (1967). Theory of Recursive Functions and Effective Computability. McGraw-Hill. Russell, K. (2003). Open-ended artificial evolution. International Journal of Computational Intelligence and Applications, 3(167).
Equivalence of Measures of Complexity Classes - Breutzmann, Lutz (1 citation) (Correct)
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H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw - Hill, New York, 1967.
Recursive Computational Depth - Lathrop, Lutz (1999) (2 citations) (Correct)
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H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw - Hill, New York, 1967.
Effective Hausdorff Dimension - Mayordomo (2000) (Correct)
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H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGraw - Hill, New York, N.Y., 1967.
Conceptualization to Develop Machine Learning Techniques.. - Grieser, Jantke, Lange (Correct)
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Advanced Elementary Formal Systems - Lange, Grieser, Jantke (2001) (Correct)
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H. Rogers Jr., Theory of Recursive Functions and Effective Computability, MIT Press, 1987.
Asymptotic Conditional Probabilities: The Non-unary Case - Adam Grove Nec (1993) (2 citations) (Correct)
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H. Rogers, Jr. Theory of Recursive Functions and Effective Computability. McGrawHill, New York, 1967.
In Case of Interval (or More General) Uncertainty, No.. - Heindl, Kreinovich.. (2001) (Correct)
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H. Rogers. Jr., Theory of recursive functions and effective computability, McGraw-Hill, N.Y., 1967.
Model Checking One Million Lines of C Code - Hao Chen Drew (2004) (2 citations) (Correct)
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Fuzzy Logic, Continuity and Effectiveness - Gerla, Biacino (2001) (Correct)
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Rogers, H.: Theory of Recursive Functions and Effective Computability, (McGraw-Hill, NewYork (1967))
Inductive Inference of ... vs. ...-Definitions for Computable.. - Case, Suraj (2002) (Correct)
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H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw Hill, New York, 1967. Reprinted, MIT Press, 1987.
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H. Rogers Jr., Theory of recursive functions and effective computability. McGraw--Hill, New York, 1967
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H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York, 1967.
Some Orbits for E - Peter Cholak Mathematics (Correct)
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H. Rogers, Jr, Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.
On Presentations of Algebraic Structures - Downey (1995) (1 citation) (Correct)
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Rogers, H. J., Theory of Recursive Functions and Effective Computability, McGraw--Hill, New York (1967).
Smallest Horn Clause Programs - Devienne, Lebègue, Parrain.. (1994) (7 citations) (Correct)
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Rogers H. "Theory of Recursive Functions and Effective Computability." The MIT Press. 1987.
Priority Arguments in Complexity Theory - Lynch, Meyer, Fischer (1972) (Correct)
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On the Logical Hierarchy of Graphs - Ly (Correct)
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H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill : Series in Higher Mathematics 1967
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