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252
What Can Be Computed Locally?
 SIAM J. Comput
, 1993
"... . The purpose of this paper is a study of computation that can be done locally in a distributed network, where "locally" means within time (or distance) independent of the size of the network. Locally Checkable Labeling (LCL) problems are considered, where the legality of a labeling can be checked l ..."
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Cited by 112 (1 self)
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. The purpose of this paper is a study of computation that can be done locally in a distributed network, where "locally" means within time (or distance) independent of the size of the network. Locally Checkable Labeling (LCL) problems are considered, where the legality of a labeling can be checked locally (e.g., coloring). The results include the following: ffl There are nontrivial LCL problems that have local algorithms. ffl There is a variant of the dining philosophers problem that can be solved locally. ffl Randomization cannot make an LCL problem local; i.e., if a problem has a local randomized algorithm then it has a local deterministic algorithm. ffl It is undecidable, in general, whether a given LCL has a local algorithm. ffl However, it is decidable whether a given LCL has an algorithm that operates in a given time t. ffl Any LCL problem that has a local algorithm has one that is orderinvariant (the algorithm depends only on the order of the processor id's). Keywords: ...
Transition Invariants
"... Proof rules for program verification rely on auxiliary assertions. We propose a (sound and relatively complete) proof rule whose auxiliary assertions are transition invariants. A transition invariant of a program is a binary relation over program states that contains the transitive closure of the tr ..."
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Cited by 90 (17 self)
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Proof rules for program verification rely on auxiliary assertions. We propose a (sound and relatively complete) proof rule whose auxiliary assertions are transition invariants. A transition invariant of a program is a binary relation over program states that contains the transitive closure of the transition relation of the program. A relation is disjunctively wellfounded if it is a finite union of wellfounded relations. We characterize the validity of termination or another liveness property by the existence of a disjunctively wellfounded transition invariant. The main contribution of
On Metric RamseyType Phenomena
"... The main question studied in this article may be viewed as a nonlinear analog of Dvoretzky's Theorem in Banach space theory or as part of Ramsey Theory in combinatorics. ..."
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Cited by 69 (39 self)
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The main question studied in this article may be viewed as a nonlinear analog of Dvoretzky's Theorem in Banach space theory or as part of Ramsey Theory in combinatorics.
Relational Transducers for Electronic Commerce
 JCSS
, 1998
"... Electronic commerce is emerging as one of the major Websupported applications requiring database support. We introduce and study highlevel declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational ..."
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Cited by 66 (11 self)
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Electronic commerce is emerging as one of the major Websupported applications requiring database support. We introduce and study highlevel declarative specifications of business models, using an approach in the spirit of active databases. More precisely, business models are specified as relational transducers that map sequences of input relations into sequences of output relations. The semantically meaningful trace of an inputoutput exchange is kept as a sequence of log relations. We consider problems motivated by electronic commerce applications, such as log validation, verifying temporal properties of transducers, and comparing two relational transducers. Positive results are obtained for a restricted class of relational transducers called Spocus transducers (for semipositive outputs and cumulative state). We argue that despite the restrictions, these capture a wide range of practically significant business models. 1 Introduction Electronic commerce is emerging as a major Webs...
On the Decision Problem for TwoVariable FirstOrder Logic
, 1997
"... We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity ..."
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Cited by 48 (1 self)
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We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO² has the finitemodel property, which means that if an FO²sentence is satisfiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO²sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO²sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO² is NEXPTIMEcomplete.
On the strength of Ramsey’s Theorem for pairs
 Journal of Symbolic Logic
, 2001
"... Abstract. We study the proof–theoretic strength and effective content denote Ramof the infinite form of Ramsey’s theorem for pairs. Let RT n k sey’s theorem for k–colorings of n–element sets, and let RT n < ∞ denote (∀k)RTn k. Our main result on computability is: For any n ≥ 2 and any computable (r ..."
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Cited by 41 (9 self)
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Abstract. We study the proof–theoretic strength and effective content denote Ramof the infinite form of Ramsey’s theorem for pairs. Let RT n k sey’s theorem for k–colorings of n–element sets, and let RT n < ∞ denote (∀k)RTn k. Our main result on computability is: For any n ≥ 2 and any computable (recursive) k–coloring of the n–element sets of natural numbers, there is an infinite homogeneous set X with X ′ ′ ≤T 0 (n). Let I�n and B�n denote the �n induction and bounding schemes, respectively. Adapting the case n = 2 of the above result (where X is low2) to models is conservative of arithmetic enables us to show that RCA0 + I �2 + RT2 2 over RCA0 + I �2 for �1 1 statements and that RCA0 + I �3 + RT2 < ∞ is �1 1conservative over RCA0 + I �3. It follows that RCA0 + RT2 2 does not imply B �3. In contrast, J. Hirst showed that RCA0 + RT2 < ∞ does imply B �3, and we include a proof of a slightly strengthened version of this result. It follows that RT2 < ∞ is strictly stronger than RT2 2 over RC A0. 1.
Repeated communication and Ramsey graphs
 IEEE Transactions on Information Theory
, 1995
"... We study the savings afforded by repeated use in two zeroerror communication problems. We show that for some random sources, communicating one instance requires arbitrarilymany bits, but communicating multiple instances requires roughly one bit per instance. We also exhibit sources where the numbe ..."
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Cited by 27 (14 self)
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We study the savings afforded by repeated use in two zeroerror communication problems. We show that for some random sources, communicating one instance requires arbitrarilymany bits, but communicating multiple instances requires roughly one bit per instance. We also exhibit sources where the number of bits required for a single instance is comparable to the source’s size, but two instances require only a logarithmic number of additional bits. We relate this problem to that of communicating information over a channel. Known results imply that some channels can communicate exponentially more bits in two uses than they can in one use. 1