#Man74# Z Manna. Mathematical Theory of Computation. McGraw-Hill, New York, 1974. #MN90# Ursula Martin and Tobias Nipkow. Ordered completion. In M. Stickel, editor, Proceedings of the Tenth International ConferenceonAutomatedDeduction,pages  Home/Search   Document Not in Database   Summary   Related Articles   Check

....constructors of logical syntactical categories, e.g. wffs and terms. Partialness allows us to achieve efficiency as the code does not have to test and decide for all the possible inputs. Extending the domain with E to handle partial functions is a well known standard technique (see, for instance, [12, 43]) One essential difference is that we have two distinct special elements, E and F. From a theoretical point of view, we could have constructed a model and a metatheory where E and F are collapsed into a unique element. The problem is that the mechanization of OT is not a finite presentation of ....

Z. Manna. Mathematical Theory of Computation. McGraw-Hill, New York, 1974.

....For each arc, this label corresponds to the union of all messages that, in a valid implementation (see section 5.3) will be transmitted along the communication channel represented by that arc. 5.3 Valid Implementations In general, of course, there are many solutions to such equations. Following [20], a valid implementation of the parallel slicing algorithm is defined as one which produces the least solution to the equations; that is, the least solution relative to the partial order of arc wise set inclusion, i.e. using v to denote the partial order, for networks L 1 and L 2 , L 1 v L 2 if ....

....every statement included in a Weiser slice will also be included using the parallel slicing algorithm. Some preliminary results are first stated and proved. 6.1 Existence of Solutions It is necessary to verify that solutions to such equations exist. This follows Kleene s first recursion theorem [20], from the fact that the functions F i , introduced in section 5.1 are monotonic 4 The possibility of describing the network in this way suggests an implementation of the algorithm by compiling the RCFG into a functional program. 14 with respect to set inclusion and hence can be solved by ....

Manna, Z. Mathematical Theory of Computation. McGraw--Hill, 1974.

....structure of the database. In the component calculus, we give primacy to these components, by letting the variables range over them. Let V be a countable set fs; t; g of component variables, or variables for short. To accommodate inapplicable nulls which are natural in SSDBs, following Manna [22], we use two kinds of equalities, namely = and : An atom of component calculus is an expression of the form 5 t:A = a, t:A : a, t:A : t:A = s:B, t:A : s:B, t v s, t v A s, t[a] 4 Note that this is stronger than saying that for every query Q expressible in L, there is an ....

Manna, Z., Mathematical Theory of Computation. McGraw-Hill, New York, Montreal, 1974.

....consider a predicate that holds for an infinite stream whenever it holds for all finite prefixes of this stream. Such a predicate is called admissible. In particular, continuous predicates (and safety predicates) are always admissible. For other classes of admissible predicates see, for example, Man74] Given an admissible predicate P and a continuous function f , it must only be shown that P(x ; f (x ) holds for all finite inputs x . This means that induction on the length of x can be used, which is often easier to handle than full Noetherian induction. All in all, we get the following ....

Z. Manna. Mathematical Theory of Computation. McGraw-Hill, 1974.

....only propagate the value of input d in to its outputs. For any dependence flow graph, we can write down a set of semantic equations over Lat in which the functions on the right hand side are monotonic and continuous. It is a well known result that such a system of equations has a least solution [Man81] Figure 10 shows these values for the program of Figure 5. The possiblepaths constants can be read off from the least solution of the semantic equations as follows. Let C : D Lat be the least solution. If t is a functional dependence, then, as in Section 2, C[t] means that the operator ....

Z. Manna. Mathematical Theory of Computation. McGraw-Hill Publishing Company, 1981.

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#Man74# Z Manna. Mathematical Theory of Computation. McGraw-Hill, New York, 1974. #MN90# Ursula Martin and Tobias Nipkow. Ordered completion. In M. Stickel, editor, Proceedings of the Tenth International ConferenceonAutomatedDeduction,pages

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