scholarly journals E-unification by means of tree tuple synchronized grammars

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Sébastien Limet ◽  
Pierre Réty
Keyword(s):  
Equational Theory ◽  
International Audience ◽  
Infinite Set ◽  
Rewrite System

International audience The goal of this paper is both to give an E-unification procedure that always terminates, and to decide unifiability. For this, we assume that the equational theory is specified by a confluent and constructor-based rewrite system, and that four additional restrictions are satisfied. We give a procedure that represents the (possibly infinite) set of solutions thanks to a tree tuple synchronized grammar, and that can decide upon unifiability thanks to an emptiness test. Moreover, we show that if only three of the four additional restrictions are satisfied then unifiability is undecidable.

scholarly journals A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups

2016 ◽  
Vol Vol. 17 no. 3 (Combinatorics) ◽  
Author(s):  
Inna Mikhaylova
Keyword(s):  
Finite Semigroup ◽  
Equational Theory ◽  
Unary Operation ◽  
Finitely Based ◽  
Infinite Basis ◽  
International Audience

International audience Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove the following theorem announced by Zhil'tsov in 2000: the equational theory of the class of all epigroups coincides with the equational theory of the class of all finite epigroups and is decidable. We show that the theory is not finitely based but provide a transparent infinite basis for it.

scholarly journals Constrained exchangeable partitions

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Alexander Gnedin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Partitions ◽  
Type Representation ◽  
International Audience ◽  
De Finetti ◽  
Infinite Set ◽  
Special Case

International audience For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

scholarly journals On the Axiomatizability of Priority

2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Luca Aceto ◽  
Taolue Chen ◽  
Willem Jan Fokkink ◽  
Anna Ingólfsdóttir
Keyword(s):  
Process Algebra ◽  
Sufficient Conditions ◽  
Equational Theory ◽  
Complete Axiomatization ◽  
Bisimulation Equivalence ◽  
Arbitrary Collection ◽  
Infinite Set ◽  
Priority Structure

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatization over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatizations using conditional equations. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatization consisting of conditional equations over the language studied in this paper. Finally, sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatization of bisimulation equivalence using conditional equations.

On the axiomatisability of priority

2008 ◽  
Vol 18 (1) ◽  
pp. 5-28 ◽  
Author(s):  
LUCA ACETO ◽  
TAOLUE CHEN ◽  
WAN FOKKINK ◽  
ANNA INGOLFSDOTTIR
Keyword(s):  
Process Algebra ◽  
Sufficient Conditions ◽  
Equational Theory ◽  
Bisimulation Equivalence ◽  
Arbitrary Collection ◽  
Infinite Set ◽  
Priority Structure

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. We prove that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatisation over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatisations using equations with action predicates as conditions. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatisation consisting of equations with action predicates as conditions over the language studied in this paper. Finally, sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatisation of bisimulation equivalence using equations with action predicates as conditions.

scholarly journals Structure of Stable Sand Piles Model

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Thi Ha Duong Phan ◽  
Thi Thu Huong Tran
Keyword(s):  
Lattice Structure ◽  
Stable Configuration ◽  
Recursive Structure ◽  
Evolution Rule ◽  
Generating Tree ◽  
International Audience ◽  
Sand Piles ◽  
Infinite Set

International audience In this paper we study a variant of the Sand Piles Model, where the evolution rule consists of the falling down of one grain to a random column and an avalanche to reach a stable configuration. We prove that the infinite set of all stable configurations have a lattice structure which is a sublattice of Young lattice. At the end, based on a discussion about avalanches, we construct a generating tree of this model and show its strongtly recursive structure.

scholarly journals Projections et cohérence de vues dans les grammaires algébriques

2008 ◽  
Vol Volume 8, Special Issue... ◽  
Author(s):  
Eric Badouel ◽  
Maurice Tchoupé Tchendji
Keyword(s):  
Global Structure ◽  
Lazy Evaluation ◽  
Document Structure ◽  
Legal Structures ◽  
International Audience ◽  
Structured Document ◽  
Partial View ◽  
Context Free ◽  
Infinite Set ◽  
Structural Aspects

International audience A complex structured document is intentionnally represented as a tree decorated with attributes. The set of legal structures is given by an abstract context-free grammar. We forget about the attributes; they are related with semantical issues that can be treated independently of the purely structural aspects that we address in this article. That intentional representation may be asynchronously manipulated by a set of independent tools each of which operates on a distinct partial view of the whole structure. In order to synchronize these various partial views, we are faced to the problem of their coherence: can we decide whether there exists some global structure corresponding to a given set of partial views and in the affirmative, can we produce such a global structure ? We solve this problem in the case where a view is given by a subset of grammatical symbols, those associated with the so-called visible syntactical categories. The proposed algorithm, that strongly relies on the mechanism of lazy evaluation, produces an answer to this problem even if partial views may correspond to an infinite set of related global structures. Un document structuré complexe est représenté intentionnellement sous la forme d'une structure arborescente décorée par des attributs. Les structures licites sont caractérisées par une grammaire algébrique abstraite. Nous faisons ici abstraction des attributs ; ces derniers sont liés à des aspects sémantiques qui peuvent être traités séparément des aspects purement structurels qui nous intéressent ici. Cette représentation intentionnelle peut être manipulée de façon indépendante et éventuellement non synchronisée par divers outils d'édition et de manipulation qui opèrent sur des vues partielles distinctes du même document. Pour la re-synchronisation de ces vues partielles nous devons résoudre le problème de leur cohérence : décider s'il existe un document correspondant à ces différentes vues et dans l'affirmative produire un tel document. Nous montrons comment résoudre ce problème dans le cas où chaque vue est associée à un sous-ensemble des symboles grammaticaux : ceux qui correspondent aux catégories syntaxiques visibles. L'algorithme proposé, qui repose fortement sur le mécanisme d'évaluation paresseuse, résout ce problème même dans le cas où chaque vue partielle correspond à un nombre infini de documents possibles.

scholarly journals Computing knowledge in equational extensions of subterm convergent theories

2020 ◽  
Vol 30 (6) ◽  
pp. 683-709
Author(s):  
Serdar Erbatur ◽  
Andrew M. Marshall ◽  
Christophe Ringeissen
Keyword(s):  
General Procedure ◽  
Security Protocols ◽  
Equational Theory ◽  
Finite Measure ◽  
Decision Procedures ◽  
Rewrite Systems ◽  
Static Equivalence ◽  
Equivalence Problems ◽  
Rewrite System

AbstractWe study decision procedures for two knowledge problems critical to the verification of security protocols, namely the intruder deduction and the static equivalence problems. These problems can be related to particular forms of context matching and context unification. Both problems are defined with respect to an equational theory and are known to be decidable when the equational theory is given by a subterm convergent term rewrite system (TRS). In this work, we extend this to consider a subterm convergent TRS defined modulo an equational theory, like Commutativity. We present two pairs of solutions for these important problems. The first solves the deduction and static equivalence problems in rewrite systems modulo shallow theories such as Commutativity. The second provides a general procedure that solves the deduction and static equivalence problems in subterm convergent systems modulo syntactic permutative theories, provided a finite measure is ensured. Several examples of such theories are also given.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Conclusion

2018 ◽  
Author(s):  
Alistair Fox
Keyword(s):  
National Identity ◽  
New Zealand ◽  
Identity Formation ◽  
Essential Role ◽  
Coming Of Age ◽  
Financial Returns ◽  
Self Recognition ◽  
International Audience ◽  
National Identity Formation

The conclusion reaffirms the essential role played by cinema generally, and the coming-of-age genre in particular, in the process of national identity formation, because of its effectiveness in facilitating self-recognition and self-experience through a process of triangulation made possible, for the most part, by a dialogue with some of the nation’s most iconic works of literature. This section concludes by point out the danger posed, however, by an observable trend toward generic standardization in New Zealand films motivated by a desire to appeal to an international audience out of consideration for the financial returns expected by funding bodies under current regimes.

Early Cinema in Scotland

2018 ◽  
Keyword(s):  
Social History ◽  
Small Towns ◽  
Early Cinema ◽  
Popular Song ◽  
Feature Film ◽  
Local Newspapers ◽  
The Social ◽  
Production History ◽  
History Of ◽  
International Audience

This collection of essays, drawn from a three-year AHRC research project, provides a detailed context for the history of early cinema in Scotland from its inception in 1896 till the arrival of sound in the early 1930s. It details the movement from travelling fairground shows to the establishment of permanent cinemas, and from variety and live entertainment to the dominance of the feature film. It addresses the promotion of cinema as a socially ‘useful’ entertainment, and, distinctively, it considers the early development of cinema in small towns as well as in larger cities. Using local newspapers and other archive sources, it details the evolution and the diversity of the social experience of cinema, both for picture goers and for cinema staff. In production, it examines the early attempts to establish a feature film production sector, with a detailed production history of Rob Roy (United Films, 1911), and it records the importance, both for exhibition and for social history, of ‘local topicals’. It considers the popularity of Scotland as an imaginary location for European and American films, drawing their popularity from the international audience for writers such as Walter Scott and J.M. Barrie and the ubiquity of Scottish popular song. The book concludes with a consideration of the arrival of sound in Scittish cinemas. As an afterpiece, it offers an annotated filmography of Scottish-themed feature films from 1896 to 1927, drawing evidence from synopses and reviews in contemporary trade journals.

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