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A Formal Definition of Intelligence Based on an Intensional Variant of Algorithmic Complexity
 In Proceedings of the International Symposium of Engineering of Intelligent Systems (EIS'98
, 1998
"... Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] ..."
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Cited by 30 (17 self)
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Machine Due to the current technology of the computers we can use, we have chosen an extremely abridged emulation of the machine that will effectively run the programs, instead of more proper languages, like lcalculus (or LISP). We have adapted the "toy RISC" machine of [Hernndez & Hernndez 1993] with two remarkable features inherited from its objectoriented coding in C++: it is easily tunable for our needs, and it is efficient. We have made it even more reduced, removing any operand in the instruction set, even for the loop operations. We have only three registers which are AX (the accumulator), BX and CX. The operations Q b we have used for our experiment are in Table 1: LOOPTOP Decrements CX. If it is not equal to the first element jump to the program top.
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 23 (2 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
Is Independence an Exception?
, 1994
"... Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable state ..."
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Cited by 19 (13 self)
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Gödel's Incompleteness Theorem asserts that any sufficiently rich, sound, and recursively axiomatizable theory is incomplete. We show that, in a quite general topological sense, incompleteness is a rather common phenomenon: With respect to any reasonable topology the set of true and unprovable statements of such a theory is dense and in many cases even corare.
Total Termination of Term Rewriting is Undecidable
 Journal of Symbolic Computation
, 1995
"... Usually termination of term rewriting systems (TRS's) is proved by means of a monotonic wellfounded order. If this order is total on ground terms, the TRS is called totally terminating. In this paper we prove that total termination is an undecidable property of finite term rewriting systems. The pr ..."
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Cited by 9 (3 self)
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Usually termination of term rewriting systems (TRS's) is proved by means of a monotonic wellfounded order. If this order is total on ground terms, the TRS is called totally terminating. In this paper we prove that total termination is an undecidable property of finite term rewriting systems. The proof is given by means of Post's Correspondence Problem. 1 Introduction Termination of term rewriting systems (TRS's) is an important property. Often termination proofs are given by defining an order that is wellfounded, and proving that for every rewrite step the value of the term decreases according this order. In many cases the order is monotonic, and it suffices to prove that l oe ? r oe for all rewrite rules l ! r and all ground substitutions oe. Standard techniques following this approach include recursive path order and KnuthBendix order, see for example [17]. It is an interesting question whether these orders are total or can be extended to a total monotonic order, or are essen...
Is Complexity a Source of Incompleteness?
 IS COMPLEXITY A SOURCE OF INCOMPLETENESS
, 2004
"... ..."
Commutation Problems on Sets of Words and Formal Power Series
, 2002
"... We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generaliza ..."
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Cited by 4 (3 self)
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We study in this thesis several problems related to commutation on sets of words and on formal power series. We investigate the notion of semilinearity for formal power series in commuting variables, introducing two families of series  the semilinear and the bounded series  both natural generalizations of the semilinear languages, and we study their behaviour under rational operations, morphisms, Hadamard product, and difference. Turning to commutation on sets of words, we then study the notions of centralizer of a language  the largest set commuting with a language , of root and of primitive root of a set of words. We answer a question raised by Conway more than thirty years ago  asking whether or not the centralizer of any rational language is rational  in the case of periodic, binary, and ternary sets of words, as well as for rational ccodes, the most general results on this problem. We also prove that any code has a unique primitive root and that two codes commute if and only if they have the same primitive root, thus solving two conjectures of Ratoandromanana, 1989. Moreover, we prove that the commutation with an ccode X can be characterized similarly as in free monoids: a language commutes with X if and only if it is a union of powers of the primitive root of X.
Primitive Solutions Of The Post Correspondence Problem
, 1996
"... s in both places for creating a very pleasant working environment. For financial support I would like to thank the Academy of Finland and Suomen Kulttuurirahasto (Elina, Sofia and Yrjo Arffman foundation). Finally, I would like to acknowledge my debt to Keijo, not only for his support, but also for ..."
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Cited by 2 (2 self)
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s in both places for creating a very pleasant working environment. For financial support I would like to thank the Academy of Finland and Suomen Kulttuurirahasto (Elina, Sofia and Yrjo Arffman foundation). Finally, I would like to acknowledge my debt to Keijo, not only for his support, but also for making some of my algorithms into programs. Real patience was needed when one of the computer runs took three weeks. Turku, February 21st, 1996 Marjo Lipponen Contents 1 Introduction 7 1.1 Basics of language theory : : : : : : : : : : : : : : : : : : : : : 9 1.2 Post Correspondence Problem : : : : : : : : : : : : : : : : : : 13 1.3 Periodic instances : : : : : : : : : : : : : : : : : : : : : : : : : 14 2 Prime Words: Basic Types 17 2.1 Primitive solutions : : : : : : : : : : : : : : : : : : : : : : : : 18 2.1.1 Primitive solutions in periodic instances : : : : : : : : 19 2.2 Ch
The Complexity of Regularity in Grammar Logics
 J. of Logic and Computation
"... A modal reduction principle of the form [i1]... [in]p ⇒ [j1]... [jn ′]p can be viewed as a production rule i1 ·... · in → j1 ·... · jn ′ in a formal grammar. We study the extensions of the multimodal logic Km with m independent K modal connectives by finite addition of axiom schemes of the above for ..."
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Cited by 1 (0 self)
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A modal reduction principle of the form [i1]... [in]p ⇒ [j1]... [jn ′]p can be viewed as a production rule i1 ·... · in → j1 ·... · jn ′ in a formal grammar. We study the extensions of the multimodal logic Km with m independent K modal connectives by finite addition of axiom schemes of the above form such that the associated finite set of production rules forms a regular grammar. We show that given a regular grammar G and a modal formula φ, deciding whether the formula is satisfiable in the extension of Km with axiom schemes from G can be done in deterministic exponentialtime in the size of G and φ, and this problem is complete for this complexity class. Such an extension of Km is called a regular grammar logic. The proof of the exponentialtime upper bound is extended to PDLlike extensions of Km and to global logical consequence and global satisfiability problems. Using an equational characterization of contextfree languages, we show that by replacing the regular grammars by linear ones, the above problem becomes undecidable. The last part of the paper presents nontrivial classes of exponential time complete regular grammar logics.
Decision Problems Concerning Prime Words and Languages of the PCP
, 1996
"... This paper investigates properties of prime words and prime languages obtained from the Post Correspondence Problem. We show that the properties of being a prime word or a finite prime language are decidable. We also present other characterization methods. ..."
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This paper investigates properties of prime words and prime languages obtained from the Post Correspondence Problem. We show that the properties of being a prime word or a finite prime language are decidable. We also present other characterization methods.
Simple Words in Equality Sets
, 1996
"... It is well known that equality sets between two morphisms possess a remarkable generative capacity: an arbitrary recursively enumerable set is obtained from an equality set by certain simple operations. Interconnections between simplicity of computations and structural primitivity of words in equali ..."
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It is well known that equality sets between two morphisms possess a remarkable generative capacity: an arbitrary recursively enumerable set is obtained from an equality set by certain simple operations. Interconnections between simplicity of computations and structural primitivity of words in equality sets have also been observed. The paper discusses recent work in this area, pointing out certain open problems and emphasizing new directions for research. TUCS Research Group