M. Nivat. Infinite words, infinite trees, infinite computations. In Foundations of Computer Science III, Mathematical Centre Tracts 109, pages 3-52, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and infinite sequences of labels. The empty sequence corresponds to and (l 0 ; l 1 ; written as l 0 l 1 in the sequel, corresponds to the sequence l 0 l 1 . If we endow the label set L with the discrete metric, then we obtain the usual metric space of sequences (as used by, e.g. Nivat in [Niv79]) The linear domains L 0 [L] L 1 [L] L 2 [L] can be seen as sets of label sequences. The branching domains B 1 [L] and B 2 [L] with L endowed with the discrete metric have been introduced by De Bakker and Zucker in [BZ83] and Van Breugel in [Bre93] respectively. In [Bre93] it has been shown ....

M. Nivat. Infinite Words, Infinite Trees, Infinite Computations. In J.W. de Bakker and J. van Leeuwen, editors, Foundations of Computer Science III, part 2: Languages, Logic, Semantics, volume 109 of Mathematical Centre Tracts, pages 3--52. Mathematical Centre, Amsterdam, 1979.

....For hA; di with A 6= a com21 plete metric space and f : A Gamma A a contracting function on hA; di we have (1) f has a unique fixed point, say x, and (2) any sequence (x n ) such that x i 1 = f(x i ) has limit x. 5. 2 Denotational semantics We only give a brief account of our approach; see [35,10,6,11] for more information on the use of metrics for denotational semantics. The semantic domain S in our case a suitable variant of TES for PA is equipped with a set Op 0 of operators that reflect the operators Op of Expr. For any fixed declaration decl, the function P 7 M(decl; P ) for P ....

M. Nivat. Infinite words, infinite trees, infinite computations. In Foundations of Computer Science III, Mathematical Centre Tracts 109, pages 3-52, 1979.

....[AN80] At the Third Advanced Course on Foundations of Computer Science, held at the Mathematical Centre in Amsterdam in August September 1978, Nivat presented joint work with Arnold about metric spaces and how they can be used to give semantics to recursive program schemes. Nivat s lecture notes [Niv79] are his most cited publication. Together with Jan van Leeuwen, Jaco de Bakker organized this course. At that time, De Bakker was completing his book [Bak80] Jeff Zucker contributed an appendix to the book and assisted in preparing the final version. In the summer of 1981, De Bakker visited ....

M. Nivat. Infinite Words, Infinite Trees, Infinite Computations. In J.W. de Bakker and J. van Leeuwen, editors, Foundations of Computer Science III, part 2: Languages, Logic, Semantics, volume 109 of Mathematical Centre Tracts, pages 3--52. Mathematical Centre, Amsterdam, 1979.

....R, DCF, CF, REK, and RE, respectively, in the sequel. Finally, we mention that there are some books as [TB70] Ei74] LS77] NP85] PP93] and, except the above mentioned papers [EH93] and [Th90] there are also some other papers surveying parts of the theory of languages (cf. CG77] HR86] [Ni79], St87b] Wi93] Notation The set f0; 1; 2; g of natural numbers is denoted by IN, and for a finite alphabet X by X (X ) we denote the set of finite words (infinite sequences) on X. For a word w 2 X 4 L. Staiger and a string b 2 X [ X let w Delta b be their ....

M. Nivat, Infinite words, infinite trees, infinite computations, Math. Centre Tracts 109 (1979), 1--52.

....The classical result due to Banach [Ban22] that a contractive function from a nonempty complete metric space to itself has a unique fixed point plays an important role in the theory of metric semantics for programming languages. Metric spaces and Banach s theorem were first employed by Nivat [Niv79] to give semantics to recursive program schemes. Inspired by the work of Nivat, De Bakker and Zucker [BZ82] gave semantics to concurrent languages by means of metric spaces. The metric spaces they used were defined as solutions of recursive domain equations. By means of Banach s theorem America ....

M. Nivat. Infinite Words, Infinite Trees, Infinite Computations. In J.W. de Bakker and J. van Leeuwen, editors, Foundations of Computer Science III, part 2: Languages, Logic, Semantics, volume 109 of Mathematical Centre Tracts, pages 3--52. Mathematical Centre, Amsterdam, 1979.

....1) let E 1 t E 2 , E 1 [t;t] E 2 . By straightforward proof one can establish that TES is closed under the operators a I : nA, jj A , and t . 5 A metric denotational semantics The approach. We only give a brief account of our approach; see [2] for a full treatment, and [15, 5, 6] for more information on the use of metrics for denotational semantics. The semantic domain S for PA is equipped with a set Op 0 of operators that reflect the operators Op of Expr. For any fixed declaration decl, the function P 7 M(hdecl; P i) is a homomorphism from (Expr; Op) to (S; Op 0 ) ....

M. Nivat. Infinite words, infinite trees, infinite computations. In Foundations of Computer Science III, Mathematical Centre Tracts 109, pages 3-52, 1979.

....These linear models are usually contrasted with branching models (cf. Gla90] In those models, the positions in the computation where a nondeterministic choice is made are administrated. Typical examples of linear metric structures proposed in the literature are sets of words (see, e.g. [Niv79]) and sets of pomsets (see, e.g. BW90] Other examples can be found in, e.g. BW91] Here, we concentrate on sets of finite and infinite words. The words over a set A of actions, denoted by A 1 , are provided with a Baire like metric [Bai09] The distance between two words is given in terms ....

M. Nivat. Infinite Words, Infinite Trees, Infinite Computations. In J.W. de Bakker and J. van Leeuwen, editors, Foundations of Computer Science III, part 2: Languages, Logic, Semantics, volume 109 of Mathematical Centre Tracts, pages 3--52. Mathematical Centre, Amsterdam, 1979.

....1 ; x 2 ; we write x 1 x 2 : xn , x 1 x 2 : xn ffi , and x 1 x 2 : respectively. If we endow SynState Theta SynStore with the discrete metric the above definition gives us the set introduced in Definition 2. 8 endowed with a Baire like [Bai09] metric as presented in, e.g. [Niv79]. The linearize operator LIN ffl removes (unsuccessful) communication attempts, ffl adds deadlock information, ffl removes the changes caused by the environment, and ffl collapses the branching structure. As the semantic sequential composition and parallel composition, LIN is defined as the ....

M. Nivat. Infinite Words, Infinite Trees, Infinite Computations. In J.W. de Bakker and J. van Leeuwen, editors, Foundations of Computer Science III, part 2: Languages, Logic, Semantics, volume 109 of Mathematical Centre Tracts, pages 3--52. Mathematical Centre, Amsterdam, 1979.

No context found.

M. Nivat. Infinite words, infinite trees, infinite computations. In Foundations of Computer Science III, Mathematical Centre Tracts 109, pages 3-52, 1979.

No context found.

M. Nivat. Infinite words, infinite trees, infinite computations. In J.W. de Bakker and J. van Leeuven, editors, Foundations of Computer Science III, Mathematical Centre Tracts 109, pages 3--52. Matematisch Centrum, Amsterdam, 1981.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC