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219
Presburger Arithmetic With Unary Predicates is ... Complete
 Journal of Symbolic Logic
, 1991
"... : We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is \Pi 1 1 complete. Adding one unary predicate is enough to get \Pi 1 1 hardness, while adding more predicates (of an ..."
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Cited by 27 (1 self)
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: We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is \Pi 1 1 complete. Adding one unary predicate is enough to get \Pi 1 1 hardness, while adding more predicates (of
Decidable theories of the ordering of natural numbers with unary predicates
 Proceedings of Computer Science Logic (CSL ’06)
, 2006
"... Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between firstorder and monadic secondorder logic. Building on the modeltheoretic composition method of Shelah, we give two characterizations of the decidable theories of t ..."
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Cited by 13 (9 self)
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Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between firstorder and monadic secondorder logic. Building on the modeltheoretic composition method of Shelah, we give two characterizations of the decidable theories
Quantum Algorithms for Finding Extrema with Unary Predicates
, 2007
"... We study the problem of finding the maximum or the minimum of a given set S = {x0, x1,... xn−1}, each element xi drawn from some finite universe U of real numbers. We assume that the inputs are abstracted within an oracle O where we can only gain information through unary comparisons in the form ”Is ..."
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We study the problem of finding the maximum or the minimum of a given set S = {x0, x1,... xn−1}, each element xi drawn from some finite universe U of real numbers. We assume that the inputs are abstracted within an oracle O where we can only gain information through unary comparisons in the form
Random Unary Predicates: Almost Sure Theories and Countable Models, Random Structures & Algorithms 13
, 1998
"... Let Un,p be the random unary predicate and Tk the almost sure firstorder theory of Un,p under the linear ordering, where k is a positive integer and n −1/k ≪ p(n) ≪ n −1/(k+1). For each k, we give an axiomatization for the theory Tk. We find a model Mk of Tk of order type roughly that of Z k and sh ..."
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Cited by 2 (2 self)
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Let Un,p be the random unary predicate and Tk the almost sure firstorder theory of Un,p under the linear ordering, where k is a positive integer and n −1/k ≪ p(n) ≪ n −1/(k+1). For each k, we give an axiomatization for the theory Tk. We find a model Mk of Tk of order type roughly that of Z k
The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 688 (73 self)
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. The scheme Ind concerns a unary predicate P, and states that: For every natural number k holdsP[k] provided the parameters satisfy the following conditions: • P[0], and • For every natural number k such thatP[k] holdsP[k+1]. The scheme Nat Ind concerns a unary predicateP, and states that: For every natural
Binary operations
 Journal of Formalized Mathematics
, 1989
"... Summary. In this paper we define binary and unary operations on domains. We also define the following predicates concerning the operations:... is commutative,... is associative,... is the unity of..., and... is distributive wrt.... A number of schemes useful in justifying the existence of the operat ..."
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Cited by 363 (6 self)
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Summary. In this paper we define binary and unary operations on domains. We also define the following predicates concerning the operations:... is commutative,... is associative,... is the unity of..., and... is distributive wrt.... A number of schemes useful in justifying the existence
Asymptotic Conditional Probabilities: The Unary Case
, 1993
"... Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fracti ..."
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Cited by 10 (3 self)
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condition on formulas ` involving unary predicate symbols only (but no equality or constant symbols), then the asymptotic conditional probability does exist and can be effectively computed. This is the case even if we place no corresponding restrictions on '. We extend this result here to the case
Unary Interpretability Logic
, 1992
"... Let T be an arithmetical theory. We introduce a unary modal operator T to be interpreted arithmetically as the unary interpretability predicate over T. We present complete axiomatizations of the (unary) interpretability principles underlying two important classes of theories. We also prove some basi ..."
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Let T be an arithmetical theory. We introduce a unary modal operator T to be interpreted arithmetically as the unary interpretability predicate over T. We present complete axiomatizations of the (unary) interpretability principles underlying two important classes of theories. We also prove some
Unary Logical Relations
"... or: Logical Predicates can be used to prove: • strong normalization • type safety (highlevel and lowlevel languages) • soundness of logics Essential idea: • A program satisfies a property if, given an input that satisfies the property, it returns an output that satisfies the property Binary Lo ..."
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or: Logical Predicates can be used to prove: • strong normalization • type safety (highlevel and lowlevel languages) • soundness of logics Essential idea: • A program satisfies a property if, given an input that satisfies the property, it returns an output that satisfies the property Binary
Asymptotic Conditional Probabilities: The Nonunary Case
 J. SYMBOLIC LOGIC
, 1993
"... Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for firstorder sentences. Given firstorder sentences ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fra ..."
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Cited by 10 (3 self)
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], if there is a nonunary predicate symbol in the vocabulary, asymptotic conditional probabilities do not always exist. We extend this result to show that asymptotic conditional probabilities do not always exist for any reasonable notion of limit. Liogon'kii also showed that the problem of deciding
Results 1  10
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219