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Ordinary Interactive SmallStep Algorithms
 I,” ACM Trans. Computational Logic
, 2004
"... This is the first in a series of papers extending the Abstract State Machine Thesis — that arbitrary algorithms are behaviorally equivalent to abstract state machines — to algorithms that can interact with their environments during a step rather than only between steps. In the present paper, we desc ..."
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Cited by 31 (16 self)
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This is the first in a series of papers extending the Abstract State Machine Thesis — that arbitrary algorithms are behaviorally equivalent to abstract state machines — to algorithms that can interact with their environments during a step rather than only between steps. In the present paper, we describe, by means of suitable postulates, those interactive algorithms that (1) proceed in discrete, global steps, (2) perform only a bounded amount of work in each step, (3) use only such information from the environment as can be regarded as answers to queries, and (4) never complete a step until all queries from that step have been answered. We indicate how a great many sorts of interaction meet these requirements. We also discuss in detail the structure of queries and replies and the appropriate definition of equivalence of algorithms. Finally, motivated by our considerations concerning queries, we discuss a generalization of firstorder logic in which the arguments of function and relation symbols are not merely tuples of elements but orbits of such tuples under groups of permutations of the argument places.
Algorithms: A quest for absolute definitions
 Bulletin of the European Association for Theoretical Computer Science
, 2003
"... y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTurin ..."
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Cited by 19 (9 self)
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y Abstract What is an algorithm? The interest in this foundational problem is not only theoretical; applications include specification, validation and verification of software and hardware systems. We describe the quest to understand and define the notion of algorithm. We start with the ChurchTuring thesis and contrast Church's and Turing's approaches, and we finish with some recent investigations.
Partial Updates: Exploration
 Journal of Universal Computer Science
, 2001
"... Abstract: The partial update problem for parallel abstract state machines has manifested itself in the cases of counters, sets and maps. We propose a solution of the problem that lends itself to an efficient implementation and covers the three cases mentioned above. There are other cases of the prob ..."
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Cited by 15 (7 self)
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Abstract: The partial update problem for parallel abstract state machines has manifested itself in the cases of counters, sets and maps. We propose a solution of the problem that lends itself to an efficient implementation and covers the three cases mentioned above. There are other cases of the problem that require a more general framework.
Strong extension axioms and Shelah’s zeroone law for choiceless polynomial time
 J. Symbolic Logic
, 2000
"... Abstract This paper developed from Shelah's proof of a zeroone law for the complexity class "choiceless polynomial time, " defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The ..."
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Cited by 6 (5 self)
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Abstract This paper developed from Shelah's proof of a zeroone law for the complexity class "choiceless polynomial time, " defined by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zeroone laws (for firstorder logic, fixedpoint logic, and finitevariable infinitary logic) are inadequate in the case of choiceless polynomial time; they must be replaced by what we call the strong extension axioms. We present an extensive discussion of these axioms and their role both in the zeroone law and in general. \Lambda Partially supported by a grant from Microsoft Research. 1 1 Introduction The BGS model of computation was defined in [4] with the intention of modeling computation with arbitrary finite relational structures as inputs, with essentially arbitrary data types, with parallelism, but without arbitrary choices. In the absence of any resource bounds, the lack of arbitrary choices makes no difference, because an algorithm could take advantage of parallelism to produce all possible linear orderings of its input and then use each of these orderings to make whatever choices are needed. But if we require the total computation time (summed over all parallel subprocesses) to be polynomially bounded, then there isn't time to construct all the linear orderings, and so the inability to make arbitrary choices really matters. In fact, it was shown in [4] that choiceless polynomial time, ~CPTime, the complexity class defined by BGS programs subject to a polynomial time bound, does not contain the parity problem: Given a set, determine whether its cardinality is even. Several similar results were proved, all depending on symmetry considerations, i.e., on automorphisms of the input structure.
Why sets?
 PILLARS OF COMPUTER SCIENCE: ESSAYS DEDICATED TO BORIS (BOAZ) TRAKHTENBROT ON THE OCCASION OF HIS 85TH BIRTHDAY, VOLUME 4800 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besi ..."
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Cited by 2 (0 self)
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Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besides, set theory seems to play a significant role in computer science; is there a good justification for that? We discuss these and some related issues.
Algorithms vs. Machines
"... Yiannis Moschovakis argues that some algorithms, and in particular the mergesort algorithm, cannot be adequately described in terms of machines acting on states. We show how to describe the mergesort algorithm, on its natural level of abstraction, in terms of distributed abstract state machines. ..."
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Cited by 1 (1 self)
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Yiannis Moschovakis argues that some algorithms, and in particular the mergesort algorithm, cannot be adequately described in terms of machines acting on states. We show how to describe the mergesort algorithm, on its natural level of abstraction, in terms of distributed abstract state machines.
Choiceless
 In Proc. of CSL 2000
, 2000
"... This paper is a sequel to [2], a commentary on [7], and an abridged version of a planned paper that will contain complete proofs of all the results presented here ..."
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This paper is a sequel to [2], a commentary on [7], and an abridged version of a planned paper that will contain complete proofs of all the results presented here
New zeroone law and strong extension axioms
 Bulletin of EATCS
, 2000
"... One of theprL4889 arL4889 in this column was devoted to thezer904; lawsfor a number of logics playingprgL88T tr00 in finite modeltheorT firrT;L# logic FO, the extension FO+LFP offir00;AL#0 logic with the least fixedpoint oper88A9 and theinfinitar logic L #,# . Recently Shelahpr v ..."
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One of theprL4889 arL4889 in this column was devoted to thezer904; lawsfor a number of logics playingprgL88T tr00 in finite modeltheorT firrT;L# logic FO, the extension FO+LFP offir00;AL#0 logic with the least fixedpoint oper88A9 and theinfinitar logic L #,# . Recently Shelahpr ved a new, powerT89 and sur4099L# zer409 law. His pr of uses socalledstral extension axioms.Her wefor ulate Shelah's zerah's law and pr ve a few facts about these axioms. In the pr cess we give a simplepr offor a"lar deviation" inequality a laCher88L 1 Shelah's ZeroOne Law Quisani: What are you doing, guys? Author: We are proving a zeroone law which is due to Shelah.
Microsoft Corporation
, 2001
"... We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets. Partially supported by NSF grant DMS–0070723 and by a grant from Microsoft R ..."
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We give an axiomatic description of parallel, synchronous algorithms. Our main result is that every such algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets. Partially supported by NSF grant DMS–0070723 and by a grant from Microsoft Research.