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Evaluation of Underdetermined Explicit Definitions
"... . The specification language VDMSL is used in the modeloriented formal method known as the Vienna Development Method. There have been a number of different dialects of this language, but a standard for the language has now been defined. The draft standard includes a dynamic semantics which, in gene ..."
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. The specification language VDMSL is used in the modeloriented formal method known as the Vienna Development Method. There have been a number of different dialects of this language, but a standard for the language has now been defined. The draft standard includes a dynamic semantics which, in general, is not executable. A given specification denotes a (possibly infinite) set of models according to the dynamic semantics. This paper illustrates how all the valid results from evaluating a given expression in all the different models can be collected. It is important to be able to do this in order to investigate the amount of looseness which is present in the given specification, such that correctness properties of the expression as a whole can be derived. We present a specification of such a loose evaluation for an executable subset of VDMSL. The subset is interesting because it also illustrates how underdeterminedness is combined with recursion in VDMSL. 1 Introduction Formal specif...
Explicit Definition of the Binary Reflected Gray Codes
 MATH
, 1997
"... It is shown that for 1 # j # n and 1 # k # 2 n ; the jth letter of the kth word of the binary reflected Gray code of length n is equal to the parity of the binomial coefficient 2 n #2 n#j #1 C #2 n #2 n#j#1 #k=2# modulo 2. Also it is shown how this observation and the usual iterative de ..."
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Cited by 3 (0 self)
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definition of the binary reflected Gray codes are revealed in a modified version of Sierpinski's gasket (Pascal's triangle modulo 2).
From Implicit via Inductive to Explicit Definitions
, 1994
"... This paper reports on a method to provide general implicit descriptions with a sound logical semantics. This method has been applied in the specification languages COLD and VVSL. ..."
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This paper reports on a method to provide general implicit descriptions with a sound logical semantics. This method has been applied in the specification languages COLD and VVSL.
Towards Proof Rules for Looseness in Explicit Definitions from VDMSL
 IN PROCEEDINGS OF THE &QUOT;INTERNATIONAL WORKSHOP ON SEMANTICS OF SPECIFICATION LANGUAGES (SOSL
, 1993
"... The modeloriented formal method called VDM contains a specification language called VDMSL. This language existed in a number of different dialects, but now a standard for the language has been prepared, including a dynamic semantics defined from a modeltheoretic point of view. Thus, it is not at ..."
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Cited by 5 (3 self)
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, it is not at all clear that the defined semantics is appropriate for deriving proof rules which reflect the semantics. This paper focus on the possible ways of defining proof rules which reflect the semantics of explicit definitions which contain looseness. The modeltheoretic view which has been chosen
A gentle tutorial on the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models
, 1997
"... We describe the maximumlikelihood parameter estimation problem and how the Expectationform of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) fi ..."
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Cited by 693 (4 self)
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) finding the parameters of a hidden Markov model (HMM) (i.e., the BaumWelch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical
Dynamic Logic
 Handbook of Philosophical Logic
, 1984
"... ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all possibl ..."
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Cited by 1012 (7 self)
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ed to be true under the valuation u iff there exists an a 2 N such that the formula x = y is true under the valuation u[x=a], where u[x=a] agrees with u everywhere except x, on which it takes the value a. This definition involves a metalogical operation that produces u[x=a] from u for all
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 2651 (32 self)
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Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis
Protecting respondents’ identities in microdata release
 In IEEE Transactions on Knowledge and Data Engineering (TKDE
, 2001
"... Today’s globally networked society places great demand on the dissemination and sharing of information. While in the past released information was mostly in tabular and statistical form, many situations call today for the release of specific data (microdata). In order to protect the anonymity of the ..."
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Cited by 512 (32 self)
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. The approach is based on the definition of kanonymity. A table provides kanonymity if attempts to link explicitly identifying information to its content map the information to at least k entities. We illustrate how kanonymity can be provided without compromising the integrity (or truthfulness
Policy gradient methods for reinforcement learning with function approximation.
 In NIPS,
, 1999
"... Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly repres ..."
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Cited by 439 (20 self)
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Abstract Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly
Explicitly
"... avoid false conditionals An infestation of termites is weakening mathematical writing. We all too often resort to wishywashy conditionals such as ‘can be ’ or ‘wish to ’ hidden within the body of sentences. Just as termites weaken a building, these conditionals erode writing by turning what should ..."
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be definite statements into weak conditionals. Get rid of them. If in your analysis or computational experiments you do something, then say so definitely; if not, say that; be explicit. There’s almost no more beautiful sight than a simple declarative sentence. Zinsser Eliminate indefiniteness. The following
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