Showing papers on "Recursively enumerable language published in 1994"
IBM1
TL;DR: This article presents simpler proofs of the same results that Landi established that it is impossible to compute statically precise alias information—either may-alias or must-alias—in languages with if statements, loops, dynamic storage, and recursive data structures.
Abstract: Alias analysis is a prerequisite for performing most of the common program analyses such as reaching-definitions analysis or live-variables analysis. Landi [1992] recently established that it is impossible to compute statically precise alias information—either may-alias or must-alias—in languages with if statements, loops, dynamic storage, and recursive data structures: more precisely, he showed that the may-alias relation is not recursive, while the must-alias relation is not even recursively enumerable. This article presents simpler proofs of the same results.
320 citations
Book•
01 Jan 1994
TL;DR: In this article, Davies introduced a general theory of elementary propositions and proved the existence of a definable well-ordering of the continuum in the context of propositional calculus, which is a necessary condition for definability for transfinite von Neumann-Godel set theory sets.
Abstract: Introduction, Martin Davies. [1] The generalized gamma functions. [51 Introduction to a general theory of elementary propositions. [14] Generalized differentiation. [17] Finite combinatory processes, Formulation I. [18] Polyadic groups. [19] The Two-Valued Iterative Systems of Mathematical Logic. [20] Absolutely unsolvable problems and relatively undecidable propositions account of an anticipation. [21] Formal reductions of the general combinatorial decision problem. [22] Recursively enumerable sets of positive integers and their decision problems. [23] A variant of a recursively unsolvable problem. [24] Note on a conjecture of Skolem. [26] Recursive unsolvability of a problem of Thue. [27] Conjuntos recurrentemente numerables de enteros positives y sus problemas de decision. [34] (with S. C. Kleene) The upper semi-lattice of degrees of recursive unsolvability. ABSTRACTS: [2] Discussion of problem 433. [3] Introduction to a general theory of elementary propositions. [4] Determination of all closed systems of truth tables. [6] On a simple class of deductive systems. [7] Visual intuition in Lobachevsky space. [8] Visual intuition in spherical and elliptic space: Einstein's finite universe. [9] A non-Weierstrassian method of analytic prolongation. [10] A new method for generalizing ex in the complex domain. [11] A simple geometric proof of the equality of the Brochardt angles of a triangle. [12] Theory of generalized differentiation. [13] The mth derivative of a function of a function calculus of mth derivatives. [15] Polyadic groups (preliminary report). [16] Finite combinatory processes. Formulation. [25] Recursive unsolvability of a problem of Thue. [28] Degrees of recursive unsolvability (preliminary report). [291 [with Samuel Linial (who later changed his name to Samuel Gulden)] Recursive unsolvability of the deducibility, Tarski's completeness, and independence of axioms problems of propositional calculus. [30] Note on a relation recursion calculus. [31] Solvability, definability, provability history of an error. [32] A necessary condition for definability for transfinite von Neumann-Godel set theory sets, with an application to the problem of the existence of a definable well-ordering of the continuum (preliminary report). [33] (with S. C. Kleene) The upper semi-lattice of degrees of recursive unsolvability. [List Permissions]
40 citations
TL;DR: It is proved that the family ℱ of all languages which are closed with respect to a right-monotone well quasi-order on a finitely generated free monoid is closed under rational operations, intersection, inverse morphisms and direct non-erasing morphisms, which implies thatℱ is open under faithful rational transductions.
Abstract: An extension of Myhill's theorem of automata theory, due to Ehrenfeucht et al. [4] shows that a subsetX of a semigroupsS is recognizable if and only ifX is closed with respect to a monotone well quasi-order onS. In this paper we prove that a similar extension of Nerode's theorem is not possible by showing that there exist non-regular languages on a binary alphabet which are closed with respect to a right-monotone well quasi-order. We give then some additional conditions under which a setX S closed with respect to a right-monotone well quasi-order becomes recognizable. We prove the following main proposition: A subsetX ofS is recognizable if and only ifX is closed with respect to two well quasi-orders<=1 and<=2 which are right-monotone and left-monotone, respectively. Some corollaries and applications are given. Moreover, we consider the family ℱ of all languages which are closed with respect to a right-monotone well quasi-order on a finitely generated free monoid. We prove that ℱ is closed under rational operations, intersection, inverse morphisms and direct non-erasing morphisms. This implies that ℱ is closed under faithful rational transductions. Finally we prove that the languages in ℱ satisfy a suitable ‘pumping’ lemma and that ℱ contains languages which are not recursively enumerable.
31 citations
TL;DR: Investigating connections between algorithmic identification in the limit of grammars from text presentation of recursively enumerable languages and standardizing operations on classes of recurring languages is the subject of this paper.
12 citations
TL;DR: The complexity of this problem when H is allowed to be countably infinite is investigated and it is shown that there exist recursive graphs with unsolvable homomorphism problems, as well as recursive graph with solvable homomorphicism problems of very high complexity.
12 citations
TL;DR: This paper shows that the algebra Pℛ of primitive recursive functions over the natural numbers has a recursive equational specification under second order initial algebra semantics, and it follows that higher orderinitial algebra specifications are strictly more powerful than first order initialgebra specifications.
Abstract: Theoretical results on the scope and limits of first order algebraic specifications can be used to show that certain natural algebras have no recursively enumerable equational specification under first order initial algebra semantics. A well known example is the algebraP? of primitive recursive functions over the natural numbers. In this paper we show thatP? has a recursive equational specification under second order initial algebra semantics. It follows that higher order initial algebra specifications are strictly more powerful than first order initial algebra specifications.
11 citations
10 Oct 1994
TL;DR: Using topological concepts in studies of the Gold paradigm of inductive inference are accumulation points, derived sets of order α (α — constructive ordinal) and compactness and Identifiability of a class U of total recursive functions with a bound α on the number of mindchanges implies U^{(\alpha + 1} =
ot 0\).
Abstract: The paper deals with using topological concepts in studies of the Gold paradigm of inductive inference. They are — accumulation points, derived sets of order α (α — constructive ordinal) and compactness. Identifiability of a class U of total recursive functions with a bound α on the number of mindchanges implies \(U^{(\alpha + 1)} =
ot 0\). This allows to construct counter-examples — recursively enumerable classes of functions showing the proper inclusion between identification types: EXα⊂EXα+1.
8 citations
TL;DR: It is proved that among computable numerations that are limit-equivalent to some positive numeration of a computable family of recursively enumerable sets, either there exists one least numeration, or there are countably many nonequivalent, minimal numerations.
Abstract: It is proved that among computable numerations that are limit-equivalent to some positive numeration of a computable family of recursively enumerable sets, either there exists one least numeration, or there are countably many nonequivalent, minimal numerations. In particular, semilattices of computable numerations for computable families of finite sets and of weakly effectively discrete families of recursively enumerable sets either have a least element or possess countably many minimal elements.
7 citations
TL;DR: A copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th(Eq*) has the same computational complexity as the true first-order arithmetic.
Abstract: We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th(Eq*) has the same computational complexity as the true first-order arithmetic.
Mathematics Subject Classification: 03D25, 03D15, 03D35.
7 citations
10 Oct 1994
TL;DR: It was conjectured in [1] that only FIN-identifiable classes are co-learnable in all r.e. numberings, and the conjecture is disproved in this paper using a sophisticated construction by V.L. Selivanov.
Abstract: Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. numberings. Hence it was conjectured in [1] that only FIN-identifiable classes are co-learnable in all r.e. numberings. The conjecture is disproved in this paper using a sophisticated construction by V.L. Selivanov.
7 citations
TL;DR: A new proof is given of the celebrated theorem of M. Davis, H. Putnam and J. Robinson concerning exponential Diophantine representation of recursively enumerable predicates by induction on the defining scheme of a partial recursive function.
14 Feb 1994
TL;DR: It is shown that if hidden sorts and functions are allowed in the specification, the converse is also true: every data type with a recursively enumerable equational theory has an ω-complete initial algebra specification with hiddensort and functions.
Abstract: An algebraic specification is called ω-complete or inductively complete if all (open as well as closed) equations valid in its initial model are equationally derivable from it, i.e., if the equational theory of the initial model is identical to the equational theory of the specification. As the latter is recursively enumerable, the initial model of an ω-complete algebraic specification is a data type with a recursively enumerable equational theory. We show that if hidden sorts and functions are allowed in the specification, the converse is also true: every data type with a recursively enumerable equational theory has an ω-complete initial algebra specification with hidden sorts and functions. We also show that in the case of finite data types the hidden sorts can be dispensed with.
TL;DR: In this paper, it was shown that it is possible to construct an r.e.t-degree with infinitely many r-degrees (i.e., 3 r-degree) with no greatest m-degree.
Abstract: In [1], Degtev constructed a non-zero r.e. tt-degree containing a single r.e. m-degree, and it is certainly possible to construct an r.e. tt-degree with no greatest m-degree (Downey, [4]) and hence an r.e. tt-degree can also have infinitely many r.e. m-degrees (Fischer [8]). Odifreddi [12, Problem 10, 13], asked if each r.e. tt-degree had to either contain one or infinitely many r.e. m-degrees. The second author in Downey [5] showed that it is possible to construct an r.e. m-degree with exactly 3 r.e. m-degrees. He also claimed that one could use the techniques of [5] to construct an r.e. tt-degrees with exactly 2 − 1 r.e. m-degrees and hence arbitrarily large numbers of r.e. m-degrees.
TL;DR: It is shown that there are strongly nonbranching degrees which are not strongly noncappable r.
Abstract: We construct an r. e. degree a which possesses a greatest a-minimal pair b0, b1, i.e., r. e. degrees b0 and b1 such that b0, b1 < a, b0 ∩ b1 = a, and, for any other pair c0, c1 with these properties, c0 ≤ bi and c1 ≤ b1-i for some i ≤ 1. By extending this result, we show that there are strongly nonbranching degrees which are not strongly noncappable. Finally, by introducing a new genericity concept for r. e. sets, we prove a jump theorem for the strongly nonbranching and strongly noncappable r. e. degrees.
Mathematics Subject Classification: 03D25.
TL;DR: An effective enumeration of all effective enumerations of classes of r.
Abstract: I introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set IE of injectively enumerable classes. It is easy to see that this set is ∑5 in the Arithmetical Hierarchy and I describe a proof for the ∑5-hardness of IE.
Mathematics Subject Classification: 03D25, 03D45.
TL;DR: Conditions under which a recursive L-structure B≃B can be constructed such that 〈B,RB〉⊬ψ for every Δ0α relation RB on B.
Posted Content•
TL;DR: The main part of the paper is concerned with instance complexity, introduced by Ko, Orponen, Schoning, and Watanabe in 1986, as a measure of the complexity of individual instances of a decision problem, and it is shown that for every r.
Abstract: We study in which way Kolmogorov complexity and instance complexity affect properties of r.e. sets. We show that the well-known 2log n upper bound on the Kolmogorov complexity of initial segments of r.e.\ sets is optimal and characterize the T-degrees of r.e. sets which attain this bound. The main part of the paper is concerned with instance complexity of r.e. sets. We construct a nonrecursive r.e. set with instance complexity logarithmic in the Kolmogorov complexity. This refutes a conjecture of Ko, Orponen, Sch"oning, and Watanabe. In the other extreme, we show that all wtt-complete set and all Q-complete sets have infinitely many hard instances.
25 Aug 1994
TL;DR: It is proved that for all non-empty, countable classes of languages C which are closed under finite variation, finite union, and under complement and for all languages L ∉ C it follows that such a super complexity core of L with respect to C exists.
Abstract: In this paper we define and study super complexity cores of languages L with respect to classes C with L ∉ C. A super complexity core S of L can be considered as an infinite set of strings for which the decision problem for L is very hard to solve with respect to the available “resources” fixed by C even for algorithms which have to compute the correct result only for all inputs x e S. For example let C = P and S be a super complexity core of L. Then S is infinite and all deterministic Turing machines M, which output 1 on input x e S ∩ L and O on input x e S ∩ Pit¯tL, need more than polynomially many steps on all but finitely many inputs x e S. We prove that for all non-empty, countable classes of languages C which are closed under finite variation, finite union, and under complement and for all languages L ∉ C it follows that such a super complexity core of L with respect to C exists. Moreover we show: Given a recursively enumerable class C of languages and a recursive language L, if there is a super complexity core of L with respect to C, then there exists a recursive super complexity core, too.
01 Apr 1994
TL;DR: In this paper, it was shown that there is an effective automorphism of 8* which is not induced by a A2-permutation, and that CD is effective iff 4D has a recursive presentation.
Abstract: We say that an automorphism 0 of A* (the lattice of recursively enumerable sets modulo the finite sets) is induced by a permutation p iff for all e, 0(We) =* p(We). A permutation h is called a presentation of 0 iff for all e, O(We) =* Wh(e) . In this paper, we will explore the degree-theoretic connections between these two notions. Using a new proof of the well-known fact that every automorphism is induced by a permutation p , we show that such a p can be found recursively in h @ 0" , where h is a presentation of 0 . The main result of the paper is to show that there is an effective automorphism of 8* which is not induced by a A2-permutation. Ever since the ground-breaking paper of Post [Po], a central object of recursion theory has been the lattice of recursively enumerable sets modulo the finite sets, g* . This object, its automorphism group Aut(g*), and their relation to the degrees of unsolvability have been extensively studied. In this paper we study the relationship between Aut(g'*) and the group of permutations of co. It has long been known (see [SoIl]) that each automorphism 1 of A* is induced by a permutation p of co. Our concern is the relationship between the complexity of d1 and the permutation that induces P. To be precise, we say D is a An+l-automorphism if D has a presentation h ( h is a permutation and for all e, 1(We) =* Wh(e)) such that h ?T on. Furthermore, we say CD is effective iff 4D has a recursive presentation. In this paper, we will examine whether every An-automorphism can be induced by a An-permutation. In Theorem 1, we show that every automorphism is induced by a permutation p, where p ?T h E 0" and h is a presentation of (D. This slightly improves Soare's result (see [Sol] or [So2, XV.2.5]) that every automorphism is induced by a permutation p, where p ?T (h ( 0')' and h is a presentation of 1'. Received by the editors October 7, 1991 and, in revised form, March 15, 1993. 1991 Mathematics Subject Classification. Primary 03D25.