What are the ultimate limits to computational techniques: verifier theory and unverifiability

[1]  Kurt Gödel,et al.  On undecidable propositions of formal mathematical systems , 1934 .

[2]  Roman V. Yampolskiy,et al.  Efficiency Theory : a Unifying Theory for Information, Computation and Intelligence , 2011, Journal of Discrete Mathematical Sciences and Cryptography.

[3]  Markus Jakobsson,et al.  Designated Verifier Proofs and Their Applications , 1996, EUROCRYPT.

[4]  G. H. Hardy,et al.  I.—MATHEMATICAL PROOF , 1929 .

[5]  M. Sørensen,et al.  Lectures on the Curry-Howard Isomorphism, Volume 149 (Studies in Logic and the Foundations of Mathematics) , 2006 .

[6]  D. Vaux,et al.  Replicates and repeats—what is the difference and is it significant? , 2012, EMBO reports.

[7]  A. Tarski Truth and proof. , 1969, Scientific American.

[8]  J. S. Moore,et al.  A Mechanized Program Verifier , 2005, VSTTE.

[9]  Gerard J. Holzmann,et al.  Economics of software verification , 2001, PASTE '01.

[10]  David J. Jilk Limits to Verification and Validation of Agentic Behavior , 2016, Artificial Intelligence Safety and Security.

[11]  Cristian S. Calude,et al.  Mathematical Proofs at a Crossroad? , 2004, Theory Is Forever.

[12]  G. Ellis Cosmology and Verifiability , 1984 .

[13]  Dorje C Brody,et al.  Hamiltonian for the Zeros of the Riemann Zeta Function. , 2016, Physical review letters.

[14]  M. Born Quantenmechanik der Stoßvorgänge , 1926 .

[15]  Felix Mühlhölzer "A Mathematical Proof Must Be Surveyable" What Wittgenstein Meant by This and What It Implies , 2006 .

[16]  H. Rice Classes of recursively enumerable sets and their decision problems , 1953 .

[17]  Michael Kohlhase,et al.  MathDox : mathematical documents on the web , 2006 .

[18]  I. Kleiner Rigor and Proof in Mathematics: A Historical Perspective , 1991 .

[19]  A. Albrecht,et al.  Origin of probabilities and their application to the multiverse , 2012, 1212.0953.

[20]  Roman V. Yampolskiy,et al.  Artificial Intelligence Safety Engineering: Why Machine Ethics Is a Wrong Approach , 2011, PT-AI.

[21]  G. Boolos The Unprovability of Consistency: An Essay in Modal Logic , 1979 .

[22]  Thomas Tymoczko Computers, Proofs and Mathematicians: A Philosophical Investigation of the Four-Color Proof , 1980 .

[23]  András Kornai,et al.  Bounding the impact of AGI , 2014, J. Exp. Theor. Artif. Intell..

[24]  Alison Abbott,et al.  Disputed results a fresh blow for social psychology , 2013, Nature.

[25]  C. Hagen,et al.  Quantum mechanical derivation of the Wallis formula for π , 2015, 1510.07813.

[26]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[27]  Roman V Yampolskiy,et al.  Safety Engineering for Artificial General Intelligence , 2012, Topoi.

[28]  Monya Baker,et al.  Cancer reproducibility project releases first results , 2017, Nature.

[29]  Roman V. Yampolskiy,et al.  What to Do with the Singularity Paradox? , 2011, PT-AI.

[30]  Max Tegmark Is “the Theory of Everything” Merely the Ultimate Ensemble Theory?☆ , 1997, gr-qc/9704009.

[31]  Richard Phillips Feynman,et al.  The Concept of Probability in Quantum Mechanics , 1951 .

[32]  Michael C. Frank,et al.  Estimating the reproducibility of psychological science , 2015, Science.

[33]  Roman V. Yampolskiy,et al.  Unethical Research: How to Create a Malevolent Artificial Intelligence , 2016, ArXiv.

[34]  Richard J. Lipton,et al.  Social processes and proofs of theorems and programs , 1977, POPL.

[35]  Stuart J. Russell,et al.  Research Priorities for Robust and Beneficial Artificial Intelligence , 2015, AI Mag..

[36]  S. Krantz The Proof is in the Pudding A Look at the Changing Nature of Mathematical Proof , 2007 .

[37]  A. Einstein Relativity: The Special and the General Theory , 2015 .

[38]  Array Александрович Кондратьев,et al.  Разработка самоприменимой системы верификации. Теория и практика , 2014 .

[39]  F. Tipler Feynman-Weinberg Quantum Gravity and the Extended Standard Model as a Theory of Everything , 2007, 0704.3276.

[40]  M. Detlefsen,et al.  The Four-color Theorem and Mathematical Proof , 1980 .

[41]  H. Everett "Relative State" Formulation of Quantum Mechanics , 1957 .

[42]  George C. Necula,et al.  Safe, Untrusted Agents Using Proof-Carrying Code , 1998, Mobile Agents and Security.

[43]  Brian Cantwell Smith,et al.  The limits of correctness , 1985, CSOC.

[44]  Leslie Lamport,et al.  How to Write a Proof , 1995 .

[45]  Jürgen Schmidhuber,et al.  Ultimate Cognition à la Gödel , 2009, Cognitive Computation.

[46]  Roman V. Yampolskiy On the Limits of Recursively Self-Improving AGI , 2015, AGI.

[47]  Edwin Coleman,et al.  The Surveyability of Long Proofs , 2009 .

[48]  Kun Peng,et al.  Efficient proof of bid validity with untrusted verifier in homomorphic e-auction , 2013, IET Inf. Secur..

[49]  Cristian S. Calude,et al.  Formal Proof: Reconciling Correctness and Understanding , 2009, Calculemus/MKM.

[50]  D. MacKenzie Slaying the Kraken: , 1999 .

[51]  Roman V. Yampolskiy,et al.  Taxonomy of Pathways to Dangerous Artificial Intelligence , 2016, AAAI Workshop: AI, Ethics, and Society.

[52]  Thomas G. Dietterich,et al.  Letter to the Editor: Research Priorities for Robust and Beneficial Artificial Intelligence: An Open Letter , 2015, AI Mag..

[53]  J. V. Bendegem,et al.  Mathematical Arguments in Context , 2009 .

[54]  P. Dirac XI.—The Relation between Mathematics and Physics , 1940 .

[55]  Roman V. Yampolskiy,et al.  Wisdom of artificial crowds algorithm for solving NP-hard problems , 2011, Int. J. Bio Inspired Comput..

[56]  I. Lakatos PROOFS AND REFUTATIONS (I)*† , 1963, The British Journal for the Philosophy of Science.

[57]  M. G. Rodd Safe AI—is this possible?☆ , 1995 .

[58]  Max Tegmark The Mathematical Universe , 2007, Foundations of Physics.

[59]  Roman Murawski Undefinability of truth. the problem of priority:tarski vs gödel , 1998 .

[60]  Kaj Sotala,et al.  Corrigendum: Responses to catastrophic AGI risk: a survey (2015 Phys. Scr. 90 018001) , 2015, Physica Scripta.

[61]  Roman V. Yampolskiy,et al.  The Space of Possible Mind Designs , 2015, AGI.

[62]  Roman V. Yampolskiy,et al.  Analysis of Types of Self-Improving Software , 2015, AGI.

[63]  D.R. Wallace,et al.  Software verification and validation: an overview , 1989, IEEE Software.

[64]  Roman V. Yampolskiy,et al.  Wisdom of Artificial Crowds—A Metaheuristic Algorithm for Optimization , 2012 .

[65]  J. Ioannidis Why Most Published Research Findings Are False , 2005, PLoS medicine.

[66]  Cristian S. Calude,et al.  Proving as a Computable Procedure , 2005, Fundam. Informaticae.

[67]  W. Heisenberg Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[68]  Roman V Yampolskiy,et al.  Responses to catastrophic AGI risk: a survey , 2014 .

[69]  James H. Fetzer Program verification: the very idea , 1988, CACM.

[70]  Ray Bert,et al.  Our Mathematical Universe: My Quest for the Ultimate Nature of Reality By Max Tegmark. New York City: Alfred A. Knopf, 2013 , 2014 .

[71]  Davide Castelvecchi,et al.  The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof , 2015, Nature.

[72]  Eugenio G. Omodeo,et al.  A 'Theory' Mechanism for a Proof-Verifier Based on First-Order Set Theory , 2002, Computational Logic: Logic Programming and Beyond.

[73]  Roman V. Yampolskiy,et al.  Turing Test as a Defining Feature of AI-Completeness , 2013, Artificial Intelligence, Evolutionary Computing and Metaheuristics.

[74]  Cristian S. Calude Incompleteness, Complexity, Randomness and Beyond , 2001, Minds and Machines.

[75]  Sanjit A. Seshia,et al.  Towards Verified Artificial Intelligence , 2016, ArXiv.

[76]  Roman V. Yampolskiy,et al.  Utility function security in artificially intelligent agents , 2014, J. Exp. Theor. Artif. Intell..

[77]  Roman V. Yampolskiy,et al.  AI-Complete CAPTCHAs as Zero Knowledge Proofs of Access to an Artificially Intelligent System , 2012 .

[78]  Tim Menzies,et al.  Verification and Validation and Artificial Intelligence , 2005, Adv. Comput..

[79]  Donald MacKenzie,et al.  The automation of proof: a historical and sociological exploration , 1995, IEEE Ann. Hist. Comput..

[80]  Samuel R. Buss,et al.  Chapter I - An Introduction to Proof Theory , 1998 .

[81]  J. Ioannidis Contradicted and initially stronger effects in highly cited clinical research. , 2005, JAMA.

[82]  Philip J. Davis,et al.  Fidelity in mathematical discourse: is one and one really two? , 1972 .

[83]  Cristian S. Calude,et al.  Computing a Glimpse of Randomness , 2002, Exp. Math..

[84]  Cristian S. Calude,et al.  From Heisenberg to Gödel via Chaitin , 2005 .

[85]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[86]  M. Baker 1,500 scientists lift the lid on reproducibility , 2016, Nature.

[87]  M. Black The Principle of Verifiability , 1934 .

[88]  Andrew W. Appel,et al.  Foundational proof-carrying code , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[89]  Natarajan Shankar,et al.  The Gradual Verifier , 2014, NASA Formal Methods.

[90]  F. Tipler The structure of the world from pure numbers , 2005 .

[91]  G. Chaitin Randomness and Mathematical Proof , 1975 .

[92]  Imre Lakatos,et al.  PROOFS AND REFUTATIONS (III)* , 1963, The British Journal for the Philosophy of Science.

[93]  Denis Ullmo,et al.  Schrödinger Approach to Mean Field Games. , 2016, Physical review letters.

[94]  Donald MacKenzie,et al.  Mechanizing Proof: Computing, Risk, and Trust , 2001 .

[95]  R. L. Wilder,et al.  The Nature of Mathematical Proof , 1944 .

[96]  E. Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint) , 1960 .

[97]  Victor W. Marek,et al.  Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer , 2016, SAT.