Z. Manna. Mathematical Theory of Computation. McGraw-Hill, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....these two challenges together. 5.5.1.1 Introduction to a Resolution based Inconsistency Detection Algorithm The resolution principle [ROB65] is an inference rule that is suitable for machineoriented deductions. We assume that the reader has some basic understanding of automatic theorem proving [CHA73, MAN74]. CHA73] provides details about the resolution principle and the linear resolution (including input resolution and unit resolution) and [LLO87] elaborates SLD resolution. To detect inconsistency, WU93a] proves a theorem about the relationship between the inconsistency of a rule base and the ....

Manna, Z., Mathematical Theory of Computation, Computer Science Series, McGraw-Hill Inc., New York, 1974.

....and concepts that we use to write down and reason about our ideas. The chapter is simply presented by using an informal extension of our everyday language to talk about mathematical objects like sets. For the terminology not explicitly shown and algebraic notation, the reader can consult [Man74, BM65, Bir67] 1.1 Basic Set Theory To de ne the basic notions that we use the standard (meta) logical notation to denote conjunction, disjunction, quanti cation and so on (and, or, for each, We will use some informal logical notation in order to stop our mathematical statements ....

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

.... up to isomorphism, the finite automaton associated with the variable X in (1) Despite its seemingly arbitrary nature, multi exit iteration is a generalization of the standard Kleene star operation whose roots may be found in the time honoured theory of flowchart schema (see, e.g. the references [19, 23]) and in the study of looping constructs in programming languages. For example, the flow of control of a process described using multi exit iteration bears strong similarity to that of a flowchart schema in normal form [13, 14] For the sake of completeness, we recall that a flowchart schema is ....

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

....the rule set is considered to be conflicting. 4.5.1.1 A Resolution based Inconsistency Detection Algorithm Resolution principle [ROB65] is an inference rules that is suitable for machineoriented deductions. We assume that the reader has some basic understanding of automatic theorem proving [MAN74, CHA73]. For details about the resolution principle and the linear resolution (including input resolution and unit resolution) the reader should refer to Chang et al. Ginsberg, and Robinson [CHA73, GIN88, ROB65] and to Lloyd [LLO87] for Ordered Linear Deduction resolution. To detect inconsistency, Wu ....

Manna, Z., Mathematical Theory of Computation, Computer Science Series, McGraw-Hill Inc., New York, 1974.

....results. 1 Introduction Several undecidability results are known about problems involving matrices [6, 14] For example, given a nite set F of matrices with integer entries, it is undecidable whether the semi group generated by M contains a matrix having a zero in the right upper corner [17], is free [11, 8] or contains the zero matrix [20] These problems have been proved to be undecidable when restricted to 3 3 matrices. But for both of them, the question of their decidability or undecidability when restricted to 2 2 matrices remains open [6] In this paper, we focus on the ....

....and v is a word of the form 01111: 11110 where the number of 1 s is any k for which k = 0. 4 Relations to other problems in the literature In this section we prove that MortQ (2) is equivalent to the entry equivalence problem studied in [15] to the zero in the corner problem studied in [17, 6], and can be linked to the problems studied in [12] When C is a matrix, C i;j denotes the entry in its ith row and jth column. 4.1 The Entry Equivalence Problem Here is a variation of Theorem 2 of [15] unlike Theorem 2 of [15] we do not suppose F to be composed of only nonsingular ....

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

.... schema capturing the class of divide and conquer programs, or a sub class thereof (e.g. those featuring an input parameter of type list, and division of that list into two shorter lists) Program schemas have been shown useful in a number of applications, such as proving properties of programs [26], teaching programming to novices [9] guiding the manual construction of programs [2, 32, 27] debugging programs [10] transforming programs [8, 11, 33] and guiding the (semi )automatic synthesis [4] of programs, be it deductive synthesis [1, 16, 18, 19, 30, 31] constructive synthesis [nobody ....

....them as higher order is that they have applications in mind, such as schemaguided program transformation [8] where some form of higher order matching between actual programs and schemas is convenient to establish applicability of the start schema of a schematic transformation. Second, Manna [26] advocates first order schemas, where actual programs are obtained via an interpretation of the (relations and functions of the) schema. This is related to the approach we advocate here, namely that a schema can also be represented as a (first order) open program (in a possibly open framework, ....

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

....the meta language, ML. The standard theorem proving tools, such as the rewriting functions, are written in ML. ML treats the terms and formulas of PPLAMBDA as data values, providing functions to build them and take them apart. Theorems are also data values. PPLAMBDA is a natural deduction logic [ manna74]: theorems are proved relative to a set of assumptions. A theorem [A ; A ] B means that the conclusion B holds whenever the assumptions A , A hold. The conclusion and assumptions are formulas. In ML, a theorem is a value of the abstract type thm, represented by a pair ....

Z. Manna, Mathematical Theory of Computation (McGraw-Hill, 1974). 34

....induction over a well founded relation is #x. #x # x. P (x # ) #x. Classically, this rule is sound if has no infinite descending chains x 1 #. W.f. induction (or Noetherian induction) is often used in program verification, and is the fundamental method for proving termination [11]. Total functions can be defined by the related 3 principle of w.f. recursion. Even if it is apparent that a relation is w.f. proving this may be di#cult. W.f. relations are most easily constructed from simpler ones, using rules that preserve the w.f. property. Later sections present Type Theory ....

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

....in the late 1960 s, who were the first to advance the idea of formulating and investigating formal systems dealing with properties of programs in an abstract setting. Research in program verification flourished thereafter with the work of many researchers, notably [Floyd, 1967] Hoare, 1969] [Manna, 1974] , and [Salwicki, 1970] The first precise development of a DL like system was carried out by [Salwicki, 1970] following [Engeler, 1967] This system was called Algorithmic Logic. A similar system, called Monadic Programming Logic, was developed by [Constable, 1977] Dynamic Logic, which ....

..... Background material on mathematical logic, computability, formal languages and automata, and program verification can be found in [Shoenfield, 1967] logic) Rogers, 1967] recursion theory) Kozen, 1997a] formal languages, automata, and computability) Keisler, 1971] infinitary logic) [Manna, 1974] (program verification) and [Harel, 1992; Lewis and Papadimitriou, 1981; Davis et al. 1994] computability and complexity) Much of this introductory material as it pertains to DL can be found in the authors text [Harel et al. 2000] There are by now a number of books and survey papers ....

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

....field of combinatorial games. Here we show that the set of solvable configurations forms a regular language, i.e. it can be recognized by a finite state automaton. In fact, this was already shown in 1991 by Plambeck ( 7] Introduction and Ch.5) and appeared as an exercise in a 1974 book of Manna [8]. More generally, B. Ravikumar showed that the set of solvable configurations on rectangular boards of any finite width is regular [9] although finding an explicit grammar seems to be di#cult on boards of width greater than 2. Thus there is little new about this result. However, it seems not to ....

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

....let Y be a subset of X.Anelementx#Xis a lower bound for Y i# x y for all y Y. Alower bound x for Y is the greatest lower bound for Y i#, for every lower bound x # for Y , x # x. When it exists, we denote the greatest lower bound for Y by #Y. We use the following two well known results [21]inthepaper:Ifxis a lower bound for Y and x Y ,then#Y=x. If #Y exists then it is unique. # Suppose that the notion of a type has been defined, and that Types is the set of all possible types. We now consider the smallest type implemented by a class. Definition 6. Consider # Types . Class P ....

Z. Manna. Mathematical Theory of Computation. McGraw-Hill, 1974. 581

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

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Z. Manna. Mathematical theory of computation. McGraw-Hill, 1974.

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

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

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

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

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Z. Manna. Mathematical theory of computation. McGraw-Hill, New York, 1974.

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

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

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

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

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

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

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

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