Results 1  10
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56
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
The TwoVariable Guarded Fragment with Transitive Relations
 In Proc. LICS'99
, 1999
"... We consider the restriction of the guarded fragment to the twovariable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing nonunary relations to occu ..."
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Cited by 39 (1 self)
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We consider the restriction of the guarded fragment to the twovariable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing nonunary relations
Ordering Constraints on Trees
, 1994
"... We survey recent results about ordering constraints on trees and discuss their applications. Our main interest lies in the family of recursive path orderings which enjoy the properties of being total, wellfounded and compatible with the tree constructors. The paper includes some new results, in par ..."
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Cited by 21 (1 self)
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, in particular the undecidability of the theory of lexicographic path orderings in case of a nonunary signature.
Decidability Issues for TwoVariable Logics with Several Linear Orders
, 2011
"... We show that the satisfiability and the finite satisfiability problems for twovariable logic, FO 2, over the class of structures with three linear orders, are undecidable. This sharpens an earlier result that FO 2 with eight linear orders is undecidable. The theorem holds for a restricted case in w ..."
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Cited by 4 (0 self)
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in which linear orders are the only nonunary relations. Recently, a contrasting result has been shown, that the finite satisfiability problem for FO 2 with two linear orders and with no additional nonunary relations is decidable. We observe that our proof can be adapted to some interesting fragments
Anonymous Hierarchical IdentityBased Encryption (Without Random Oracles). In: Dwork
 CRYPTO 2006. LNCS,
, 2006
"... Abstract We present an identitybased cryptosystem that features fully anonymous ciphertexts and hierarchical key delegation. We give a proof of security in the standard model, based on the mild Decision Linear complexity assumption in bilinear groups. The system is efficient and practical, with sm ..."
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Cited by 119 (10 self)
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Σ ∈ N in unary, and the hierarchy's maximum depth D ∈ N, the setup algorithm first generates a bilinear instance 1. Select 7 + 5 D + D 2 random integers modulo p (some of them forcibly nonzero): 2. Publish G and the system parameters Pub ∈ G T × G 2 (1+D) (2+D) given by: 3. Retain the master
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 ..."
Abstract

Cited by 10 (3 self)
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, Halpern, and Koller [22], in the general case, asymptotic conditional probabilities do not always exist, and most questions relating to this issue are highly undecidable. These results, however, all depend on the assumption that ` can use a nonunary predicate symbol. Liogon'kii [31] shows that if we
The Number of Similarity Relations and the Number of Minimal Deterministic Finite Cover Automata
"... Abstract. Finite Deterministic Cover Automata (DFCA) can be obtained from Deterministic Finite Automata (DFA) using the similarity relation. Since the similarity relation is not an equivalence relation, the minimal DFCA for a finite language is usually not unique. We count the number of minimal DFCA ..."
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DFCA that can be obtained from a given minimal DFA with n states by merging the similar states in the given DFA. We compute an upper bound for this number and prove that in the worst case (for a nonunary alphabet) it is d
Deterministic Pushdown Automata and Unary Languages
, 2009
"... The simulation of deterministic pushdown automata defined over a oneletter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a ..."
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Cited by 1 (0 self)
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succinct than finite automata. In order to state this result, we investigate the conversion of deterministic pushdown automata into contextfree grammars. We prove that in the unary case the number of variables in the resulting grammar is strictly smaller than the number of variables needed in the case
Unique Decipherability in the Monoid of Languages: an Application of Rational Relations
, 2008
"... We attack the problem of deciding whether a finite collection of finite languages is a code, that is, possesses the unique decipherability property in the monoid of finite languages. We investigate a few subcases where the theory of rational relations can be employed to solve the problem. The case ..."
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. The case of unary languages is one of them and as a consequence, we show how to decide for two given finite subsets of nonnegative integers, whether they are the nth root of a common set, for some n ≥ 1. We also show that it is decidable whether a finite collection of finite languages is a Parikh code
Sequentiality in Bounded Biorders
 FUNDAMENTA INFORMATICAE
, 2005
"... We study a notion of bounded stable biorder, showing that the monotone and stable functions on such biorders are sequential. We construct bounded biorder models of a range of sequential, higherorder functional calculi, including unary PCF, (typed and untyped) callbyvalue and lazy λcalculi, and ..."
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Cited by 2 (0 self)
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calculi, and nondeterministic SPCF. We prove universality and full abstraction results for these models by reduction to the case of unary PCF, for which we give a simple new argument to show that any orderextensional and sequential model is universal.
Results 1  10
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56