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WHEN ARE TWO ALGORITHMS THE SAME?
"... than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists. 1. ..."
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than the programs that implement them. The natural way to formalize this idea is that algorithms are equivalence classes of programs with respect to a suitable equivalence relation. We argue that no such equivalence relation exists. 1.
Exact Exploration and Hanging Algorithms ⋆
"... Abstract. Recent analysis of sequential algorithms resulted in their axiomatization and in a representation theorem stating that, for any sequential algorithm, there is an abstract state machine (ASM) with the same states, initial states and state transitions. That analysis, however, abstracted from ..."
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Abstract. Recent analysis of sequential algorithms resulted in their axiomatization and in a representation theorem stating that, for any sequential algorithm, there is an abstract state machine (ASM) with the same states, initial states and state transitions. That analysis, however, abstracted from details of intrastep computation, and the ASM, produced in the proof of the representation theorem, may and often does explore parts of the state unexplored by the algorithm. We refine the analysis, the axiomatization and the representation theorem. Emulating a step of the given algorithm, the ASM, produced in the proof of the new representation theorem, explores exactly the part of the state explored by the algorithm. That frugality pays off when state exploration is costly. The algorithm may be a highlevel specification, and a simple function call on the abstraction level of the algorithm may hide expensive interaction with the environment. Furthermore, the original analysis presumed that state functions are total. Now we allow state functions, including equality, to be partial so that a function call may cause the algorithm as well as the ASM to hang. Since the emulating ASM does not make any superfluous function calls, it hangs only if the algorithm does. [T]he monotony of equality can only lead us to boredom. —Francis Picabia 1
What Is an Algorithm
 SOFSEM, Lecture Notes in
"... We present a twopart exposition on the notion of algorithm and foundational analyses of computation. The first part is below, and the second is here: ..."
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We present a twopart exposition on the notion of algorithm and foundational analyses of computation. The first part is below, and the second is here:
THE PHYSICAL CHURCHTURING THESIS AND THE PRINCIPLES OF QUANTUM THEORY
, 2012
"... As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is ..."
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As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information — and proves that the physical ChurchTuring thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal nontrivial interplay between theoretical physics symmetries and computability assumptions.
Three Paths to Effectiveness
"... For Yuri, profound thinker, esteemed expositor, and treasured friend. Abstract. Over the past two decades, Gurevich and his colleagues have developed axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in a new framework of abstract state ..."
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For Yuri, profound thinker, esteemed expositor, and treasured friend. Abstract. Over the past two decades, Gurevich and his colleagues have developed axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in a new framework of abstract state machines. Recently, this approach was extended to suggest axiomatic foundations for the notion of effective computation over arbitrary countable domains. This was accomplished in three different ways, leading to three, seemingly disparate, notions of effectiveness. We show that, though having taken different routes, they all actually lead to precisely the same concept. With this concept of effectiveness, we establish that there is – up to isomorphism – exactly one maximal effective model across all countable domains.
Applicationsensitive access control evaluation: Logical foundations. (Under review
"... Abstract—Access control schemes come in all shapes and sizes, which makes choosing the right one for a particular application a challenge. Yet today’s techniques for comparing access control schemes completely ignore the setting in which the scheme is to be deployed. In this paper, we present a form ..."
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Abstract—Access control schemes come in all shapes and sizes, which makes choosing the right one for a particular application a challenge. Yet today’s techniques for comparing access control schemes completely ignore the setting in which the scheme is to be deployed. In this paper, we present a formal framework for comparing access control schemes with respect to a particular application. The analyst’s main task is to evaluate an access control scheme in terms of how well it implements a given access control workload (a formalism that we introduce to represent an application’s access control needs). One implementation is better than another if it has stronger security guarantees, and in this paper we introduce several such guarantees: correctness, homomorphism, ACpreservation, safety, administrationpreservation, and compatibility. The scheme that admits the implementation with the strongest guarantees is deemed the best fit for the application. We demonstrate the use of our framework by evaluating two workloads on ten different access control schemes. Index Terms—access control; evaluation; state machine; parameterized expressiveness I.
Towards a ChurchTuringthesis for infinitary computations
 Electronic Proceedings of CiE 2013
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Around the physical ChurchTuring thesis: Cellular automata, formal languages, and the principles of quantum theory
 In Proc. 6th International Conference on Language and Automata Theory and Applications (LATA 2012, A Coruña
, 2012
"... Abstract. The physical ChurchTuring thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density ..."
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Abstract. The physical ChurchTuring thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density of information. This principle itself questions our formulation of quantum theory, in particular the choice of a field for the scalars and the origin of the infinite dimension of the vector spaces used as state spaces1. 1 The ChurchTuring Thesis and Its Various Forms 1.1 Why a Thesis? It is a quite common situation in mathematics, that a notion, first understood intuitively, receives a formal definition at some point. For instance, the notion of a real number has been understood intuitively in geometry, for instance as the length of a segment, before it has been formally defined in the 19th century, by Cauchy and Dedekind. Another example is the notion of an algorithm, that has been understood intuitively for long, before a formal definition of the notion of a
EVOLVING MULTIALGEBRAS UNIFY ALL USUAL SEQUENTIAL COMPUTATION MODELS
, 2010
"... Abstract. It is wellknown that Abstract State Machines (ASMs) can simulate “stepbystep” any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all AS ..."
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Abstract. It is wellknown that Abstract State Machines (ASMs) can simulate “stepbystep” any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs. We modify Gurevich’s notion of ASM to that of EMA (“Evolving MultiAlgebra”) by replacing the program (which is a syntactic object) by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via “literal identifications ” to slight extensions of the usual machine models and also to grammar models. Though we modify these models, we keep their computation approach: only some contingencies are modified. Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms. Contents
Honest Universality
, 2012
"... We extend the notion of universality of a function, due to Turing, to arbitrary (countable) effective domains, taking care to disallow any cheating on the part of the representations used. universal function, representation, encoding, effectiveness, comKeywords: putability 1 ..."
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We extend the notion of universality of a function, due to Turing, to arbitrary (countable) effective domains, taking care to disallow any cheating on the part of the representations used. universal function, representation, encoding, effectiveness, comKeywords: putability 1