Pith. sign in

REVIEW 3 major objections 5 minor 45 references

Evolutionary Automata and Deep Evolutionary Computation

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that evolutionary automata with unbounded generations accept every formal language over a fixed alphabet, placing evolutionary computation beyond Turing machines.

desk verdict Nonconstructive hardcoding and a self-conceded gap sink the central expressiveness claim; the paper is mostly a restatement of prior work. read the letter →

arxiv 2411.15008 v2 pith:RXWK7UKU submitted 2024-11-22 cs.NE cs.CL

Eugene Eberbach This is my paper · ORCID
classification cs.NEcs.CL
keywords EvolutionaryAlgorithmsAutomataDeepComputingExpressivenessEvolutionofUndecidableProblemsSuper-TuringModelsComputationTerminalLanguages
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to put evolutionary computation on the same analytical footing as classical automata theory by modeling it as an evolutionary automaton: a possibly infinite sequence of automata, each generation handing its population to the next. Its central aim is to prove this model is far more expressive than Turing machines—specifically, that evolutionary finite automata in terminal mode accept every language over a fixed alphabet, decidable or not. The result is meant to show that deep evolutionary computation, evolution over an unbounded number of generations, can in principle handle Turing-machine undecidable problems and matches the expressiveness of interaction machines and oracle machines. A reader should care because the argument recasts what computation can do if evolution is allowed to run forever, although the proof is nonconstructive and the paper acknowledges that limitation.

What carries the argument

The object doing the work is the evolutionary automaton itself—a possibly infinite sequence $E = \{E[0], E[1], E[2], \ldots\}$ of level automata, each applying variation and selection to a population and handing the next generation to the following component. Acceptance in terminal mode means that some component eventually accepts the input word, so the sequence as a whole behaves like an infinite union of the languages of its components. The proof of Theorem 5.3 rests on the per-word finite automaton $A_w$, which recognizes exactly the single string $w$ and passes all other strings to the next generation; this reduces language membership to the question of whether some component recognizes the word. The paper calls the unbounded-generation regime deep evolutionary computation, drawing the analogy to deep neural networks with many layers.

What would settle it

Run the Theorem 5.3 construction on the diagonalization language: since the proof assigns one component automaton per word, an effective recipe that outputs those automata would enumerate an undecidable set. Demonstrating that no such recipe can exist, because it would contradict the diagonalization language's non-recursively-enumerable definition, settles the claim as existential rather than algorithmic; demonstrating a recipe would refute the paper's own Remark 5.4.

Watch

Extended reading notes

Core claim

The central claim is Theorem 5.3: in terminal mode, the class of languages accepted by evolutionary finite automata ($TL(EFA)$) coincides with the class of all languages over the alphabet $\Sigma$—including languages that are recursively enumerable but not recursive, and languages that are not recursively enumerable at all. For each word $w$ in a target language $L$, the proof builds a finite automaton $A_w$ that accepts exactly $w$ and forwards every other word to the next component; taking the sequence $E = \{A[t] = A_w : w \in L\}$ makes the evolutionary automaton accept the union of these singletons, namely $L$. The paper presents this as showing evolutionary finite automata are more expressive than Turing machines and equally expressive with interaction machines and Turing o-machines. Remark 5.4 concedes the catch: for an undecidable $L$ the components cannot actually be constructed, so the theorem establishes the existence of a recognizing sequence without giving a method to find it.

Load-bearing premise

The proof assumes that for any language $L$, including an undecidable one, one may simply take the sequence of automata $\{A_w : w \in L\}$ even though no effective procedure is given for producing or verifying that sequence.

Editorial extensions

If this is right

  • All regular, context-free, and context-sensitive languages over a given alphabet are accepted by evolutionary finite automata, not merely some of them.
  • Evolutionary finite automata, interaction machines, and Turing o-machines have the same terminal expressiveness; the paper conjectures the same for neural networks, cellular automata, the $\pi$-calculus, and the $-calculus.
  • Evolutionary computation with finitely many generations has exactly the power of its component automata; only unbounded generations create the jump beyond Turing machines.
  • Elitist evolutionary algorithms with complete variation operators converge to global optima as the number of generations goes to infinity, with a proof the paper presents as much simpler than earlier Markov-chain arguments.
  • If Theorem 5.3 holds, deep evolutionary computation is in principle a super-Turing model, able to express solutions to undecidable problems rather than only approximating them.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Read as a claim about possible structures rather than algorithms, the theorem is a nonconstructive existence result: without an effective enumeration of $L$, the automaton sequence cannot be built, so the paper does not supply a procedure that solves undecidable problems.
  • If the component sequence had to be produced by a fixed finite program, the terminal language would be recursively enumerable, which suggests the gap between expressiveness and solvability is exactly the gap between existence and effective construction.
  • The practical moral is not that infinite evolution literally decides the undecidable, but that increasing the generation horizon is a finite approximation of a limit process, analogous to adding layers to a network.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces evolutionary automata, defined as sequences of component automata E[t] that process successive population generations, and studies their terminal-mode acceptance. The main claim is Theorem 5.3: the terminal languages of evolutionary finite automata coincide with the class of all languages over a finite alphabet, from which the paper infers that evolutionary computation can solve Turing-machine undecidable problems. The paper also compares evolutionary automata with other super-Turing models, proposes a complexity hierarchy (p-, e-, a-, i-decidable), and gives a new proof of asymptotic convergence for evolutionary algorithms with elitism and complete variation operators.

Significance. If Theorem 5.3 were constructive, it would establish a striking super-Turing expressiveness result for a simple evolutionary model, with consequences for the theoretical foundations of evolutionary computation. The paper is also useful in explicitly distinguishing terminal acceptance from recursive decidability and in situating evolutionary automata among other super-Turing frameworks. However, the central proof is nonconstructive and circular, as the paper itself concedes in Remark 5.4 and Section 8, so the claimed consequence that evolutionary computation can solve undecidable problems is not established. The framework may have pedagogical value, but the main contribution does not survive scrutiny.

major comments (3)
  1. [Section 5, Theorem 5.3] The proof defines, for each word w in L, a finite automaton A_w accepting exactly w, and then takes 'any sequence E = {A[t] = A_w, w in L}' of such automata. For an infinite language L this requires an enumeration of L to build the sequence, and for an undecidable L no effective enumeration exists. More fundamentally, the construction is circular under the terminal-mode semantics of Definition 5.1: an input u is accepted by E iff some component A_u accepting u occurs in E, which is determined by u in L. Thus membership in L is presupposed by the choice of E rather than computed by it.
  2. [Section 5, Remark 5.4 and Section 8] Remark 5.4 explicitly states that for undecidable non-recursive languages 'we cannot construct such finite automata, thus we will not know that this specific EFA encodes the language,' and Section 8 concedes that constructing input strings for undecidable languages 'requires to solve the membership problem for undecidable languages' and is 'not done yet.' These statements directly undermine the inference drawn from Theorem 5.3 that evolutionary computation can solve Turing-machine undecidable problems. The theorem at best provides a nonconstructive set-theoretic existence statement about arbitrary infinite sequences of finite automata, not a demonstration that any effective evolutionary process decides membership.
  3. [Section 4, Remark 4.4] The definition of evolutionary automata intentionally leaves unspecified how the component automata E[t] evolve from generation to generation, and Remark 4.4 states that 'that is not needed for the proof of expressiveness of evolutionary automata.' This is another indication that the expressiveness claim of Theorem 5.3 is an artifact of freely choosing the component sequence to match the target language. Without a specification of how E[t] is produced or selected, the model does not supply an algorithm that could be said to solve a problem, so the super-Turing consequences drawn from the theorem do not follow.
minor comments (5)
  1. [Section 3.1, Theorem 3.1] The proof of Theorem 3.1 is essentially a restatement of the assumptions: if variation operators are complete, then by definition every search point, including a global optimum, is reached with positive probability, and infinite time plus elitism then guarantee retention of the optimum. The argument is correct but tautological; the paper should identify what new content beyond the earlier proofs it cites is being claimed.
  2. [Corollary 5.4 and Remark 5.4] There are several typos, including 'langauges' for 'languages' in the title of Corollary 5.4 and 'vey simple' for 'very simple' in Remark 5.4; these should be corrected.
  3. [Definition 5.1 and proof of Theorem 5.3] The acceptance condition 'there is a number t' should specify whether the component automaton must terminate on the given input or merely reach an accepting state while possibly continuing; the proof of Theorem 5.3 uses transducers that output non-accepted words to the next component, so a formal output convention is needed.
  4. [Remarks 4.2 and 4.3] The text uses 'obvolute' where 'convoluted' is intended, and 'Meale/Moore' should be 'Mealy/Moore' throughout; these spelling errors should be fixed.
  5. [Section 7, Definition 7.1] The classes p-, e-, a-, i-decidable are listed without proof of separation or of membership of standard problems; as they stand, they are descriptive categories rather than a complexity theory, and this should be acknowledged explicitly.

Circularity Check

1 steps flagged · score 8.0 of 10

Theorem 5.3 builds the EFA from the target language L itself, so 'EFA accepts L' holds by construction; Remark 5.4 concedes the components cannot be constructed for undecidable L, leaving the 'solve undecidable problems' claim unsupported.

  1. self definitional [Section 5, Theorem 5.3 (Proof)]
    "To do this, for each wordw, we build a finite automatonAw that given a wordw as its input, accepts only the wordw, and given any other wordu, it outputs u, which goes as input to the next finite automaton in the EFA A. In both cases, the automaton A comes to a terminal state pending that there exists Au accepting u, otherwise u is rejected. Then taking any sequence E = {A[t] = Aw, w ∈ L} of such automata, we obtain the necessary evolutionary finite automaton A."

    The recognizer E is selected directly from the target language L: component A_w is included exactly when w ∈ L. Under terminal-mode acceptance, u is accepted iff some A_u occurs in E, which by construction happens iff u ∈ L. Thus TL(E) = L is not derived by evolutionary computation; it is inserted into the definition of E. For undecidable L no effective enumeration or construction of the components is supplied, so the proof cannot support the paper's claim that evolutionary computation can solve TM-undecidable problems.

full rationale

The central expressiveness result, Theorem 5.3, is circular in the specific sense that the component sequence E is chosen from the very language L whose acceptance is to be established. The proof defines E = {A[t] = A_w : w ∈ L}, where A_w accepts only w. Then a word u is accepted in terminal mode exactly when some A_u appears in E, which is exactly when u ∈ L. No evolutionary mechanism, fitness function, or effective construction is involved; the membership question is presupposed by the selection of components. The same pattern appears in Theorems 5.1 and 5.2, where A[t] is chosen to accept the t-th word of the target language, making the union of accepted words equal to the language by construction. The paper's own Remark 5.4 concedes the nonconstructivity: 'For undecidable non-recursive languages ... we cannot construct such finite automata, thus we will not know that this specific EFA encodes the language ...'. Section 8 further admits that solving the membership problem for undecidable languages is 'not done yet' and that only the existence of an encoding is proved. There is a legitimate set-theoretic reading of Theorem 5.3: every countable language is a countable union of singleton regular languages, so an EFA whose component sequence is allowed to be an arbitrary, possibly noncomputable, family of finite automata can indeed have any language as its terminal language. But that is a definitional closure property, not a demonstration that evolutionary computation can decide or solve undecidable problems. The score reflects that the paper's principal predictive claim reduces by construction to its own input, even though parts of the paper, such as the convergence-in-the-limit argument for elitist complete-search EAs, are independent and not circular.

Assumptions & free parameters 0 free parameters · 4 assumptions · 1 invented entities

There are no fitted numeric parameters. The proof depends on three conceptual choices: the unrestricted freedom to choose the sequence of automata (Remark 4.4), the terminal-acceptance definition as the notion of solving (Definition 5.1), and a nonconstructive enumeration of the target language. These choices, rather than fitted constants, carry the argument.

assumptions (4)
  • standard math Every language L over a finite alphabet can be enumerated to index the automaton sequence (Theorem 5.3 proof).
    Relies on the countability of finite words and the existence of an enumeration of any countable subset, without requiring effectiveness.
  • domain assumption Terminal acceptance by one component in the infinite sequence counts as solving the problem.
    Definition 5.1 defines acceptance as existence of some t where A[t] accepts; this is the paper's chosen notion of solving, not the standard halting-based one.
  • ad hoc to paper The evolution mechanism between components E[t] can be left unspecified and can be chosen freely to fit the language.
    Remark 4.4 intentionally leaves how E[t] changes open, which is what permits the hardcoded sequence in Theorem 5.3.
  • domain assumption Infinite computations are legitimate models and can be extrapolated to natural evolution.
    The paper's 'infinity principle' and Section 8 extrapolate expressiveness to natural evolution without a formal definition of natural evolution.
invented entities (1)
  • Evolutionary automaton (evolutionary K-machine)
    purpose: To model evolutionary computation as an infinite sequence of automata that can evolve, yielding claimed hypercomputational expressiveness.
    The model is a mathematical construct with no falsifiable prediction outside the paper; its main property (accepting all languages) is obtained by construction rather than by an independent mechanism.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Evolutionary Automata and Deep Evolutionary Computation." pith.science (2026). https://pith.science/paper/RXWK7UKU

@misc{pith2026241115008,
  author       = {Pith},
  title        = {Pith review of: Evolutionary Automata and Deep Evolutionary Computation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RXWK7UKU}},
  note         = {Machine review of arXiv:2411.15008}
}
read the original abstract

Evolution by natural selection, which is one of the most compelling themes of modern science, brought forth evolutionary algorithms and evolutionary computation, applying mechanisms of evolution in nature to various problems solved by computers. In this paper we concentrate on evolutionary automata that constitute an analogous model of evolutionary computation compared to well-known evolutionary algorithms. Evolutionary automata provide a more complete dual model of evolutionary computation, similar like abstract automata (e.g., Turing machines) form a more formal and precise model compared to recursive algorithms and their subset - evolutionary algorithms. An evolutionary automaton is an automaton that evolves performing evolutionary computation perhaps using an infinite number of generations. This model allows for a direct modeling evolution of evolution, and leads to tremendous expressiveness of evolutionary automata and evolutionary computation. This also gives the hint to the power of natural evolution that is self-evolving by interactive feedback with the environment.

Figures

Figures reproduced from arXiv: 2411.15008 by the authors.

Figure 1
Figure 1. Evolutionary Automaton REMARK 4.1. Note that our approach is inspired, but not equivalent to Lary Fogel’s EP [24]. EP uses iterative evolutionary algorithms of the class of finite automata that operate on the set of finite automata X. On the other hand, evolutionary automata can use evolutionary algorithms from the class of arbitrary abstract automata, e.g., finite automata, pushdown automata, linearly bounded autom… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages

  1. [8]

    Evolutionary Automata: Expressiveness and Convergence of Evolution- ary Computation, Computer Journal, 55(9), pp.1023-1029, doi: dx.doi.org/10.1093/comjnl/bxr099

    Burgin, M.; Eberbach, E., 2012. Evolutionary Automata: Expressiveness and Convergence of Evolution- ary Computation, Computer Journal, 55(9), pp.1023-1029, doi: dx.doi.org/10.1093/comjnl/bxr099. 24 E. Eberbach / Evolutionary Automata

    work page doi:10.1093/comjnl/bxr099 2012

  2. [1]

    What is computation

    Aho, A.. Computation and Computational Thinking, Ubiquity ACM symposium “What is computation”, Ubiquity Magazine, V ol.2011, Issue January, Article no.1, Jan. 2011, doi: 10.1145/1922681.1922682

    arXiv 2011

  3. [2]

    (eds.): Handbook of Evolutionary Computation, Oxford University Press, Oxford

    Back, T.; Fogel, D.B.; and Michalewicz, Z., 1997. (eds.): Handbook of Evolutionary Computation, Oxford University Press, Oxford

    work page 1997

  4. [3]

    Burgin, M.. 1999. Super-recursive Algorithms as a Tool for High Performance Computing, Proc. of the High Performance Computing Symposium, San Diego, pp.224-228

    work page 1999

  5. [4]

    Computers and their Applications

    Burgin, M., 2003. Cluster Computers and Grid Automata, in Proceedings of the ISCA 17th International Conference “Computers and their Applications”, International Society for Computers and their Applica- tions, Honolulu, Hawaii, pp. 106-109

    work page 2003

  6. [5]

    Burgin, M., 2005: Superrecursive Algorithms, Springer, New York

    work page 2005

  7. [6]

    Burgin, M.; Eberbach, E., 2009. On Foundations of Evolutionary Computation: An Evolutionary Au- tomata Approach, in Handbook of Research on Artificial Immune Systems and Natural Computing: Ap- plying Complex Adaptive Technologies (Hongwei Mo, Ed.), IGI Global, Hershey, Pennsylvania, pp.342- 360

    work page 2009

  8. [7]

    Bounded and Periodic Evolutionary Machines, in Proc

    Burgin, M.; Eberbach, E., 2010. Bounded and Periodic Evolutionary Machines, in Proc. 2010 Congress on Evolutionary Computation (CEC’2010), Barcelona, Spain, pp.1379-1386

    work page 2010

Show all 45 references
  1. [9]

    Recursively Generated Evolutionary Turing Machines and Evolutionary Automata, in (ed

    Burgin, M.; Eberbach, E., 2013. Recursively Generated Evolutionary Turing Machines and Evolutionary Automata, in (ed. Xin-She Yang): Artificial Intelligence, Evolutionary Computing and Metaheuristics, In the Footsteps of Alan Turing, Studies in Computational Intelligence, vol....

    2013

  2. [10]

    An Unsolvable Problem of Elementary Number Theory, American Journal of Mathematics, vol.58, 1936, 345-363

    Church A.. An Unsolvable Problem of Elementary Number Theory, American Journal of Mathematics, vol.58, 1936, 345-363

    1936

  3. [11]

    What is computation

    Denning, P.. What Have We Said About Computation? Closing Statement, Ubiquity ACM sympo- sium “What is computation”, Ubiquity Magazine, V ol.2011, Issue April, Article no.1, April 2011, doi: 10.1145/1967045.1967046

    2011

  4. [12]

    On Expressiveness of Evolutionary Computation: Is EC Algorithmic?, Proc

    Eberbach, E., 2002. On Expressiveness of Evolutionary Computation: Is EC Algorithmic?, Proc. 2002 World Congress on Computational Intelligence WCCI’2002, Honolulu, HI, pp.564-569

    2002

  5. [13]

    Beyond Turing Machines, Bulletin of the European Association for Theo- retical Computer Science EATCS, BEATCS no

    Eberbach E.,Wegner P., 2003. Beyond Turing Machines, Bulletin of the European Association for Theo- retical Computer Science EATCS, BEATCS no. 81, Oct. 2003, pp.279- 304

    2003

  6. [14]

    Turing’s Ideas and Models of Computation, in: (ed

    Eberbach, E.; Goldin, D.; Wegner, P., 2004. Turing’s Ideas and Models of Computation, in: (ed. Ch.Teuscher) Alan Turing: Life and Legacy of a Great Thinker, Springer-Verlag, pp.159-194

    2004

  7. [15]

    Toward a theory of evolutionary computation, BioSystems, v

    Eberbach, E., 2005. Toward a theory of evolutionary computation, BioSystems, v. 82, pp. 1-19

    2005

  8. [16]

    Eberbach, E., 2007: The $-Calculus Process Algebra for Problem Solving: A Paradigmatic Shift in Han- dling Hard Computational Problems, Theoretical Computer Science, vol.383, no.2-3, pp.200-243 (doi: dx.doi.org/10.1016/j.tcs.2007.04.012)

    2007 doi

  9. [17]

    Evolutionary Automata as Foundation of Evolutionary Computation: Larry Fogel Was Right, Proc

    Eberbach, E.; Burgin, M., 2009. Evolutionary Automata as Foundation of Evolutionary Computation: Larry Fogel Was Right, Proc. 2009 Congress on Evolutionary Computation CEC’2009, Trondheim, pp.2149-2156

    2009

  10. [18]

    Unsinkable

    Eberbach E., Mikkilineni R.. Cloud Computing with DNA Cognitive Architecture in the Context of Tur- ing’s “Unsinkable” Titanic Machine, Proc. of 23rd IEEE Intern. Conf. on Enabling Technologies: Infras- tructure for Collaborative Enterprises WETICE 2014, Track on Convergence o...

    2014 doi

  11. [19]

    On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus, Fun- damenta Informaticae, IOS Press, 188(2):63-90(2022), https://doi.org.10.3233/FI-222142

    Eberbach, E., 2022. On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus, Fun- damenta Informaticae, IOS Press, 188(2):63-90(2022), https://doi.org.10.3233/FI-222142

    2022 doi

  12. [20]

    Theoretical and Foundational Problems in Information Studies

    Eberbach, E., 2022. Undecidability and Complexity for Super-Turing Models of Computation, Proceed- ings Journal 2022, 81, 123, https://doi.org/103390/proceedings2022081123, Presented at the Conference “Theoretical and Foundational Problems in Information Studies”, IS4SI Summit...

    2022

  13. [21]

    Blondie24: Playing at the Edge of AI, Morgan Kaufmann Publishers

    Fogel, D.B., 2002. Blondie24: Playing at the Edge of AI, Morgan Kaufmann Publishers

    2002

  14. [22]

    An Introduction to Evolutionary Computation, Tutorial, Congress on Evolutionary Computation (CEC’2001), Seoul, Korea

    Fogel, D.B., 2001. An Introduction to Evolutionary Computation, Tutorial, Congress on Evolutionary Computation (CEC’2001), Seoul, Korea

    2001

  15. [23]

    Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, IEEE Press

    Fogel, D.B., 1995. Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, IEEE Press

    1995

  16. [24]

    Walsh, M.J., 1966

    Fogel, L.J., Owens, A.J. Walsh, M.J., 1966. Artificial Intelligence Through Simulated Evolutions, John Wiley, New York

    1966

  17. [25]

    ¨Uber formal unentscheidbare S ¨atze der Principia Mathematica und verwander Systeme, Monatschefte f¨ur Mathematik und Physik, 38:173-198, 1931

    G ¨odel K.. ¨Uber formal unentscheidbare S ¨atze der Principia Mathematica und verwander Systeme, Monatschefte f¨ur Mathematik und Physik, 38:173-198, 1931. E. Eberbach / Evolutionary Automata 25

    1931

  18. [26]

    Adaptation in Natural and Artificial Systems, Univ

    Holland, J.H., 1975. Adaptation in Natural and Artificial Systems, Univ. of Michigan Press, Ann Arbor, MIT Press, 2nd ed

    1975

  19. [27]

    Introduction to Automata Theory, Languages, and Com- putation, Addison Wesley, Boston/San Francisco/New York

    Hopcroft, J.E.; Motwani R.; Ullman, J.D., 2001. Introduction to Automata Theory, Languages, and Com- putation, Addison Wesley, Boston/San Francisco/New York

    2001

  20. [28]

    Algorithm Design, Pearson/Addison-Wesley, Boston/San Francisco/New York

    Kleinberg, J.; Tardos, E., 2006. Algorithm Design, Pearson/Addison-Wesley, Boston/San Francisco/New York

    2006

  21. [29]

    Koza, J., 1992: Genetic Programming I, II, III, MIT Press, 1992, 1994, 1999

    1992

  22. [30]

    Introduction to Set Theory and Topology, PWN, Warsaw, 1977

    Kuratowki K., 1977. Introduction to Set Theory and Topology, PWN, Warsaw, 1977

    1977

  23. [31]

    Michalewicz, Z., 1996: Genetic Algorithms + Data Structures = Evolution Programs, Third edition, Springer-Verlag

    1996

  24. [32]

    How to Solve It: Modern Heuristics, 2nd edition, Springer-Verlag

    Michalewicz, Z.; Fogel, D.B., 2004. How to Solve It: Modern Heuristics, 2nd edition, Springer-Verlag

    2004

  25. [33]

    Schema Theorems for GA/GP, Tutorial, Congress on Evolutionary Computation (CEC’2001), Seoul, Korea

    Poli, R., 2001. Schema Theorems for GA/GP, Tutorial, Congress on Evolutionary Computation (CEC’2001), Seoul, Korea

    2001

  26. [34]

    Evolutionstrategie: Optimierung technischer Systeme nach Prinizipien der biologis- chen Evolution, Fromman-Holzboog Verlag, Stuttgart

    Rechenberg, I., 1973. Evolutionstrategie: Optimierung technischer Systeme nach Prinizipien der biologis- chen Evolution, Fromman-Holzboog Verlag, Stuttgart

    1973

  27. [35]

    Refenes A.N., Eberbach E., McCabe S.C., Treleaven P.C. 1989. PARLE: A Parallel Target Language for Integrating Symbolic and Numeric Processing, Proc. Conf. on Parallel Architectures and Languages Europe PARLE’89, Lect. Notes in Computer Science 366, Springer-Verlag, Eindhoven,...

    1989

  28. [36]

    1995, Artificial Intelligence: A Modern Approach, (1st ed.)Prentice Hall, New Jersey

    Russell S., Norvig P. 1995, Artificial Intelligence: A Modern Approach, (1st ed.)Prentice Hall, New Jersey

    1995

  29. [37]

    Convergence analysis of canonical genetic algorithms, IEEE Trans

    Rudolph, G., 1994. Convergence analysis of canonical genetic algorithms, IEEE Trans. Neural Networks: Special Issue on EC, v. 5:1, pp.96-101

    1994

  30. [38]

    Hypercomputation: Computing Beyond the Church-Turing Barrier, Springer- Verlag

    Syropoulos, A., 2008. Hypercomputation: Computing Beyond the Church-Turing Barrier, Springer- Verlag

    2008

  31. [39]

    Computational Completeness of Interaction Machines and Turing Machines, Proc

    Wegner, P.; Eberbach, E.; Burgin, M., 2012. Computational Completeness of Interaction Machines and Turing Machines, Proc. The Turing Centenary Conference, Turing-100, Alan Turing Centenary, EasyChair Proc. in Computing, EPiC vol. 10 (ed. A. V oronkov), Manchester, UK, pp.405-414

    2012

  32. [40]

    No free lunch theorem for optimization, IEEE Trans

    Wolpert, D.H.; Macready, W.G., 1997. No free lunch theorem for optimization, IEEE Trans. Evol. Com- put., V ol. 1, No. 1, pp.67-82

    1997

  33. [41]

    The Fifth Generation Computer

    Tohru Moto-oka, Masaru Kitsuregawa. The Fifth Generation Computer. The Japanese Challenge, John Wiley & Sons, 1985

    1985

  34. [42]

    On Computable Numbers, with an Application to the Entscheidungsproblem, Proc

    Turing, A., 1936. On Computable Numbers, with an Application to the Entscheidungsproblem, Proc. London Math. Soc., 42-2, 1936, pp.230-265; A correction, ibid, 43, 1937, pp.544-546

    1936

  35. [43]

    Systems of Logic based on Ordinals, Proc

    Turing, A., 1939. Systems of Logic based on Ordinals, Proc. London Math. Soc. Series 2, 45, 1939, pp.161-228

    1939

  36. [44]

    Intelligent Machinery, 1948, in Collected Works of A.M

    Turing, A., 1948. Intelligent Machinery, 1948, in Collected Works of A.M. Turing: Mechanical Intelli- gence, ed.D.C.Ince, Elsevier Science, 1992

    1948

  37. [45]

    Principia Mathematica, vol.1, 1910, vol.2, 1912, vol.3, 1913, Cambridge Univ

    Whitehead A.N., Russell B.. Principia Mathematica, vol.1, 1910, vol.2, 1912, vol.3, 1913, Cambridge Univ. Press, London

    1910

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.