Rice's theorem - Factbites

Rice's theorem - Factbites
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Topic: Rice's theorem

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	Rice
		Rice's theorem Rice's theorem (also known as The Rice-Myhill-Shapiro theorem) is an important result in the theory of r...
		Rice Township, Pennsylvania Rice Township is a township located in 2000 census, the township had a total population of 2...
		Rice Township, Minnesota Rice Township is a township located in 2000 census, the township had a total population of 134....
	www.brainyencyclopedia.com /topics/rice.html

	Computing Papers on Theorem
		Some of the principal Theorems include the existence of a universal program, the unsolvability of the halting problem (there does not exist a mechanical means of checking for infinite loops in the executions of programs), and Rice`s Theorem.
		The sweeping conclusion of Rice`s Theorem is the impossibility of algorithmically analyzing computer programs to determine in which cases a given property is possessed by the function computed by the program.
		Unfortunately, after GÂ¨del announced his famed incompleteness Theorem in o 1931 stating that it is impossible to have a formalism that can help us to reach all truths and only truths, we nally realized that we had gone a long way in ghting a battle that was impossible to win.
	computing.breinestorm.net /Theorem (3065 words)

	CS 611, v3.0: Exams Archives
		Be comfortable with the s-m-n theorem, the recursion theorem and Rice's theorem.
		Then it proves some useful theorems, like Rice's theorem, the SMN theorem and the recursion theorem, then it uses those theorems in proofs of other theorems.
		For the proof project, you need to turn in revised definitions, revised theorem statements and scratchwork for your proof.
	lal.cs.byu.edu /cs611/archives/exams (1226 words)

	Citations: Mellin Transforms and Asymptotics: Finite Differences and Rice's Integrals - Flajolet, Sedgewick (ResearchIndex)
		Mellin transforms and asymptotics: finite differences and Rice's integrals.
		Flajolet, P., Sedgewick, R., Mellin transform and asymptotics: finite differences and Rice's integrals, Special volume on mathematical analysis of algorithms.
		As should become apparent in this chapter, Mellin transform are also part of the arsenal of asymptotic methods for discrete mathematics and the analysis of algorithms.
	citeseer.ist.psu.edu /context/64925/75787 (1226 words)

	fim.txt
		For example, the theorem could be confirmed by drawing, re-arranging, and counting dots on a page, or by using grains of rice on a table, or by using a calculator.
		Theorem nine indicates that each of the random events which make up an individual's experiences could then be determined by a finite number of those bits which could provide a choice indistinguishable to that individual from the ideal probability generated by the infinitary mathematics.
		Theorem one can also be used to illustrate some of the ways in which mathematical facts can be represented and confirmed by physical processes.
	www.poco.phy.cam.ac.uk /~mjd1014/fim.txt (4846 words)

	Contract Soundness for Object-Oriented Languages from Rice University White Papers at Builder UK
		Pushing the analogy further, we state and prove a contract soundness theorem that captures the essential properties of contract enforcement.
		We use the theorem to illustrate how most existing tools suffer from a fundamental flaw and how they can be improved.
		Contract Soundness for Object-Oriented Languages from Rice University White Papers at Builder UK Home
	uk.builder.com /whitepapers/0,39026692,60030704p-39000929q,00.htm (4846 words)

	URCS Theory Technical Reports
		We also prove a Rice-style theorem for NP, namely that every nontrivial language property of NP sets is NP-hard, and we prove that every P-constructibly semi-switching counting property of circuits is PP-hard.
		Since the Kaemper-AFK Theorem and Yap's Theorem are used in the literature as bridges in a variety of results---ranging from the study of unique solutions to issues of approximation---our results implicitly strengthen all those results.
		We eliminate some special cases from the proofs of two theorems in which a machine instantiating a many-query reduction to a p-selective set is made to use only one query.
	www.cs.rochester.edu /trs/theory-trs.html (16130 words)

	Search Results for pi[~n]on - Encyclopædia Britannica
		Rice University, Houston, U.S. Resource exploring concepts like binomial distribution, normal distribution, central limit theorem, and confidence interval, with the help of a simulation and study questions.
		French mathematician who proved the prime number theorem, which states that as n approaches infinity, (n) approaches, where (n) is the number of positive prime numbers not greater than n.
		One of the supreme achievements of 19th-century mathematics was the prime number theorem, and it is worth a brief digression.
	www.britannica.com /search?query=pi[~n]on&submit=Find&source=MWTEXT (500 words)

	Search Results for binomial - Encyclopædia Britannica
		Rice University, Houston, U.S. Resource exploring concepts like binomial distribution, normal distribution, central limit theorem, and correction for continuity, with the help of a demonstration and study questions.
		Two of the most widely used discrete probability distributions are the binomial and Poisson.
		The binomial probability mass function (equation 6) provides the probability that x successes will occur...
	www.britannica.com /search?query=binomial&submit=Find&source=MWTEXT (444 words)

	Articles - GÃ¶del's incompleteness theorem
		This result was later generalised in the field of recursive functions to Rice's theorem which shows that all non-trivial properties of recursive functions are undecidable, i.e.
		In principle, GÃ¶del's theorems still leave some hope: it might be possible to produce a general algorithm that for a given statement determines whether it is undecidable or not, thus allowing mathematicians to bypass the undecidable statements altogether.
		GÃ¶del's theorems are theorems in first-order logic, and must ultimately be understood in that context.
	www.oldion.com /articles/Incompleteness_theorem (444 words)

	New lecture series honors minority scientists
		Both Blackwell, who is professor emeritus of mathematics at U.C. Berkeley, and Tapia, who is the Noah Harding Professor of Computational and Applied Mathematics at Rice, will attend the event, which will conclude with a banquet in their honor.
		His name is attached to a theorem in statistics, the Rao-Blackwell theorem, which is important in estimation theory and tests of hypotheses.
		Blackwell was elected to the National Academy of Sciences in 1965.
	www.news.cornell.edu /Chronicle/00/4.20.00/Blackwell-Tapia_lectures.html (444 words)

	Parr, R. G. - List of Publications - Component of : Early Ideas in the History of Quantum Chemistry.
		[145] Use of the virial theorem in construction of potential energy functions for diatomic molecules.
		[70] Integral Hellmann-Feynman theorem, baniers to internal rotation, and iso-electronic processes.
		Parr, R. Bernstein, H. Gutowsky, S. Rice, H. Simmons, and 0.
	www.quantum-chemistry-history.com /Parr_Dat/Parr_Publ1.htm (444 words)

	Course 6.045/18.400: Automata, Computability, and Complexity
		Rice's Theorem: A photocopy of Lecture 34 from Kozen was passed out.
		The LaTex shell requires the use of 6045preamble.tex.
		A LaTeX shell for Homework 0, this should make it easier to LaTeX your homework solutions.
	theory.lcs.mit.edu /classes/6.045/spring03/materials.html (445 words)

	Eureka, A page of Mathematical Recreations
		More recently, San Diego homemaker Marjorie Rice took up the question of which types of shapes can tile the plane, developing a fruitful, unorthodox notation to solve previously unanswered questions.
		One notable instance is Pierre de Fermat, whose 'Last Theorem' confounded Mathematicians for 350 years and led to the construction of whole new disciplines intended to lay a foundation for the solution.
		Mathematical icon Paul Erdos relished the story of a twelve year old boy who instantly solved a problem he, Erdos, had needed ten minutes to solve.
	matcmadison.edu /mbertrand/mab/eureka/eureka.html (445 words)

	Computability Complexity Logic Book
		Halting problem K. Special cases of Rice's 69 theorem.
		Theorem of 481 Cook, theorem of Henschen & Wos, polynomial equivalence of Horn- and network-complexity, theorem of Stockmeyer.
		Grzegorczyk hierarchy theorem Equivalence of 197 the characterisation by growth-rate (limited recursion, excursus on Ackermann branches), recursion- and loop- depth, computing-time complexity from Kleene normal form with polynomially bounded or R3-coding functions.
	www.di.unipi.it /~boerger/cclbookcontents.html (788 words)

	halting problem - Article and Reference from OnPedia.com
		Yet another, quite amazing, consequence of the undecidability of the halting problem is Rice's theorem which states that the truth of any non-trivial statement about the function that is defined by an algorithm is undecidable.
		The concepts raised by Gdel's incompleteness theorems are very similar to those raised by the halting problem, and the proofs are quite similar.
		This weaker form differs from the standard statement of the incompleteness theorem by asserting that a complete, consistent and sound axiomatization of all statements about natural numbers is unachievable.
	www.onpedia.com /encyclopedia/halting-problem (2611 words)

	CISC 601 - Computer & Information Science - UD
		Unlimited register machines, Turing machines, partial recursive functions; Church-Turing thesis; algorithmically unsolvable problems and diagonalization; primitive recursive functions; Kleene normal form theorem; universal programs; recursively enumerable and recursive sets; recursion theorem; Rice's theorem.
		Deterministic and non-deterministic finite automata and their equivalence to regular expressions, pumping lemma and Myhill-Nerode theorem; context-free grammars and languages, and the corresponding pushdown automata.
		At least one course in which the student was required to prove theorems.
	www.cis.udel.edu /graduate/courses/601.php (133 words)

	j05cmp.html
		The above proof of Rice's theorem for Joy is adapted from a proof for recursive functions in {Phillips92}.
		The recursion theorem traces its ancestry to Epimenides, Russell and Grelling (for
		One consequence ot the S-m-n theorem is the diagonalisation theorem: There is a recursive function taking as argument the Gödel number of a function which takes at least one parameter, and giving as value the Gödel number of the function obtained from the given one by substituting itself for the parameter.
	www.latrobe.edu.au /philosophy/phimvt/joy/j05cmp.html (6457 words)

	Dr Benedikt Loewe: Recursion Theory (1st Semester 2003/2004)
		Recursive Functions (Soare, Chapter I): Primitive Recursive Functions, Turing Machines, Kleene Normal Form Theorem, Enumeration Theorem, s-m-n Theorem, The Halting Problem, Reducibilities, Rice's Theorem, Myhill's Isomorphism Theorem
		If you're interested, you can go on and use your version of the Normal Form Theorem to prove the relativized Enumeration Theorem and the relativized s-m-n Theorem.
		Give a formal definition of that notion and prove the corresponding theorem.
	staff.science.uva.nl /~bloewe/2003-I-RT.html (6457 words)

	Internet Electronic Journal of Molecular Design
		The method is based on the Hellmann-Feynman theorem, using the perturbed anharmonic oscillator wavefunctions, and the conceptual approach of Sceats and Rice.
		The Hellmann-Feynman theorem, in combination with the stationary perturbation theory in the non-degenerate case for the representation of anharmonic oscillator perturbed (by hydrogen bonding) wavefunction, is applied.
		A novel theoretical method that enables extraction of the function describing the dependence of the decoupled X-H(D) intramolecular potential on the hydrogen bond strength from experimental frequency-structure correlation equations is proposed.
	www.biochempress.com /av01_0285.html (6457 words)

	Rice Course Schedule, Fall 2003: Mathematics (MATH)
		Other topics include first order hyperbolic systems, Cauchy-Kowalewski theorem, potential theory, Dirichlet and Neumann problems, integral equations, elliptic equations.
		Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem.
		MATH 101 SINGLE VARIABLE CALCULUS I Credits 3.00 Fall 03 * DISTRIBUTION COURSE: GROUP III Differentiation, extrema, Newton's method, integration, fundamental theorem of calculus, area, volume, natural logarithm, exponential.
	www.rice.edu /projects/courses/2003fall/MATH.html (6457 words)

	Gauss-Markov Theorem and Wiener Filtering
		Clayton Scott and Rob Nowak, "Gauss-Markov Theorem and Wiener Filtering," Connexions, May 24, 2004, http://cnx.rice.edu/content/m11454/1.6/.
		Scott, C., and Nowak, R. Gauss-Markov Theorem and Wiener Filtering.
		Scott, C.; Nowak, R. Gauss-Markov Theorem and Wiener Filtering, Connexions Web site.
	cnx.rice.edu /content/m11454/latest/history (172 words)

	Doctoral Degree - CS Dept
		Computability Theory: Loop programs, primitive recursive functions, partial recursive functions, Godel numbering universal program, Halting problem, recursive sets, recursively enumerable sets, decidability and undesirability, many to one reducibility and completeness results, s-m-n theorem, recursion theorem, Rice theorems (both).
		Time and space bounded computation, time and space hierarchy theorems, complexity classes P, NP, Co-NP, L, NL, polynomial time hierarchy and basic known/unknown results, relativization and oracle computations.
		Complexity Theory: Blum's axioms, gap theorem, speedup theorem, basic theorems about abstract complexity measures.
	www.cs.pitt.edu /education/grad/prelim/theory (266 words)

	hello, may I help you?
		Also some on (un)com- putability (Rice and theorem and Kleene fixpoint) but fundamentally nothing else, notably nothing on lambda calculus, and nothing even resembling re- flection, apart from Godel theorem.
		first order mathematic logic, Godel theorem, and I am studying modal and fuzzy logic and some cathegory theory.
		I am starting a PhD at Politecnico di Milano and I would like to push my research towards something concerning reflection, but I need to better understand what computational reflection is and implies before trying to do that.
	lists.tunes.org /archives/tunes/2001-March/003079.html (165 words)

	Instructional Demos
		Dice rolling simulation (Can be used to demonstrate the central limit theorem.)
		Normal distribution movie, Interactive graph of normal distribution
		A small effect can make a large difference
	davidmlane.com /hyperstat/Instructional_Demos.html (165 words)

	CS 380/480 Course Syllabus
		Rice's Theorem, Cook's Theorem and the Chomsky Hierarchy
		Regular Languages, Finite Automata and the Myhill-Nerode Theorem
	www.cs.utk.edu /~langston/courses/cs380/syllabus.html (101 words)

	Linux-kernel mailing list archive 2000-01,: Re: Super Lint (was: Unexecutable Stack / Buffer Overflow Exploits...)
		> But from rice's theorem follows that for any given super-lint, there is a
		I wanted just to point out some utterly wrong argument (Goedels
		> > Goedel tells you about axiomatic systems which encompass both ARITHMETIC
	www.cs.helsinki.fi /linux/linux-kernel/Year-2000/2000-01/0239.html (303 words)

	Rice Math Course Web Pages
		Math 111: The Fundamental Theorem of Calculus, Anne Papakonstantinou.
		Math 111: Fundamental Theorem of Calculus (Section 1)
		Math 211: Ordinary Differential Equations and Linear Algebra, all sections.
	math.rice.edu /Courses/previous.html (303 words)

	Computability Complexity Logic Book
		Recursion theorem: 58 fixed-point meaning (theorem of Rice), recursion meaning (implicit definitions: recursive enumeration of Fprim, injective translation functions in Goedel numbering, isomorphism theorem for Goedel numberings, self- reproducing programs), parametric effective version with infinitely many fixed points.
		114 Reduction concepts (theorem of Post), index sets (theorem of Rice and Shapiro, Sn-complete program properties), creativityand S1-completeness (theorem of Myhill), simple sets (theorem of Dekker and Yates), priority method (theorem of Friedberg and Mucnik), complexity of the arithmetical truth concept.
		Simple reductions of K. Decision problems of 71 universal computing systems, Post's correspondence problem, Domino problem.
	www.di.unipi.it /~boerger/cclbookcontents.html (303 words)

	j05cmp.html
		The recursion theorem leads in a few steps to Rice's theorem, see {Rogers67}, which encapsulates all the bad news of computability theory: for example the halting problem, or the impossibility of writing programs which check other programs - implementation, student exercises - for correctness.
		The above proof of Rice's theorem for Joy is adapted from a proof for recursive functions in {Phillips92}.
		One consequence ot the S-m-n theorem is the diagonalisation theorem: There is a recursive function taking as argument the Gödel number of a function which takes at least one parameter, and giving as value the Gödel number of the function obtained from the given one by substituting itself for the parameter.
	www.latrobe.edu.au /philosophy/phimvt/joy/j05cmp.html (6457 words)

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