Synchronous Tree Research Articles

About Semantic Action Refinement

A notion of semantic action refinement is defined both on Synchronization Trees and on Causal Trees, a class of trees recently devised for giving a full account to causality [DD89]. The branching bisimulation, as introduced in [GW89a], is shown to be preserved under semantic action refinement. As a by-product, the axiomatization of the congruence induced by branching bisimulation which was given in [GW89a] is still valid under action refinement. Both results hold for Synchronization Trees and, with the needed extensions, for Causal Trees.

Does Asynchronous Fruit Ripening Avoid Satiation of Seed Dispersers?: A Field Test

Asynchronous ripening of fruits within individual, temperate, summer—fruiting, bird—dispersed plants has been proposed to be an adaptation to avoid satiation of dispersers when they are not abundant. I tested a prediction of this hypothesis by manipulating ripening synchrony on individual Amelanchier arborea trees and comparing ripe fruit removal rates from these trees to paired controls. Artificially synchronous ripe fruit displays were created by cutting of unripe fruit and replacing them with ripe fruit. Fruit removal was faster for the manipulated, synchronous tree in three pairs, slower in two pairs, and not significantly different in five other pairs, suggesting that synchronous displays did not satiate dispersers. This unexpected result is attributed to violation of the unstated assumption that dispersers are relatively sedentary in their foraging in the summer and do not concentrate at large fruit displays. In this study the major frugivore of A. arborea, the Cedar Waxwing (Bombycilla cedrorum), foraged widely in flocks of 2—6; other reports reveal that some other frugivorous bird species also forage widely in the summer. This nonterritorial foraging implies that the arrival of dispersers is temporally unpredictable from the perspective of each plant, and it is this temporal unpredictability that may favor asynchronous ripening in plants lacking adaptations for ripe fruit persistence.

Competition and Tree Death

can flatten all the trees in their paths. More subtle events of synchronous tree mortality, such as those caused by defoliating insects or fungal diseases, may attract attention because of the ghostly skeletons that remain. But these dramatic forms of tree mortality are the exception; most tree deaths go unnoticed. At best only a few of the many thousands of seedlings produced by a typical mature tree can survive and grow to achieve canopy position and reproductive status. Most die as a direct or indirect consequence of failure to compete successfully for light, water, or soil nutrients. This form of tree death has come to be called natural thinning, or self-thinning when applied to a relatively even-aged population of a single species. These terms contrast the process with artificial thinning, where less vigorous or unwanted trees are selectively removed by man. Although individually the deaths attributable to natural

A logic for the description of non-deterministic programs and their properties

We present a logic, called Synchronization Tree Logic (STL), for the specification and proof of programs described in a simple term language obtained from a constant Nil by using a set A of unary operators, a binary operator + and recursion. The elements of A represent names of actions, + represents non-deterministic choice, and Nil is the program preforming no action. The language of formulas of the logic proposed, contains the term language used for the description of programs, i.e., programs are formulas of the logic. This provides a uniform frame to deal with programs and their properties as the verification of anassertion t ⊨ f (t is a program, f is a formula) is reduced to the proof of the validity of the formula t ⊃ f. We propose a sound and under some conditions complete deductive system for synchronization tree logics and discuss their relation with modal logics used for the specification of programs.

On the relationships between Scott domains, synchronization trees, and metric spaces

We use Scott's idea of information systems to provide a complete partial order semantics for concurrency involving Milner's synchronization tree model. Several connections are investigated between different models; our principal technique in establishing these connections is the use of compact metric space methods.

A logical characterization of observation equivalence

Brookes and Rounds (1983) showed that a finitary formal language (‘regular trace language’, or Reg-TL, for short) which allowed a certain kind of quantification using regular subsets of Σ ∗ was not strong enough to distinguish all pairs of observationally inequivalent synchronization trees. In the present paper we extend this result to show that there is no class C of subsets of Σ ∗ such that C -TL can distinguish all pairs of observationally inequivalent synchronization trees. We then give a characterization of observation equivalence in terms of an infinitary formal language S-TL( ω). This language is obtained as an extension of the language S-TL (‘singleton trace language’) of Hennessy and Milner by the addition of a connective of ω-conjunctions of formulas of finite bounded deoth.

Synchronization trees

Synchronization trees are a concrete underlying model for much of the work on concurrency. They are trees with labelled arcs: the nodes represent states, the arcs occurrences of events and their labels how the events can synchronize with other events in the environment. The many different ways in which events are allowed to synchronize are captured abstractly by the concept of a synchronization algebra. It says which pairs of labelled events can combine to form an event of synchronization and what label the synchronization event carries. Synchronization trees are trees with arcs labelled by elements of a synchronization algebra. Our approach is based on a natural definition of morphism of trees which essentially expresses how the occurrence of events in one process imply the synchronized occurrence of events in another. Well-known operations on trees arise as categorical constructions. For example, a sum construction is a coproduct on synchronization trees while many familiar parallel compositions of synchronization trees are restrictions of the product in the underlying category of trees. The constructions are continuous with respect to a natural complete partial order structure on trees so one obtains denotational semantics as synchronization trees to a wide range of parallel programming languages, based on the constructions with recursion, in a routine manner by varying the synchronization algebra. Isomorphism of synchronization trees induces a basic congruence on terms of the language. We present a complete proof system for the congruence restricted to nonrecursive terms. The categories of trees are generalized to categories of transition systems. The pleasant categorical set-up which exists between the categories of trees and transition systems makes possible a smooth translation between operational semantics expressed in terms of transition systems and denotational semantics expressed in terms of trees.

Connections between two theories of concurrency: Metric spaces and synchronization trees

A connection is established between the semantic theories of concurrency and communication in the works of de Bakker and Zucker, who develop a denotational semantics of concurrency using metric spaces instead of complete partial orders, and Milner, who develops an algebraic semantics of communication based upon observational equivalence between processes. His rigid synchronization trees (RSTs) are endowed with a simple pseudometric distance induced by Milner's weak equivalence relation and the quotient space is shown to be complete. An isometry between this space and the solution to a domain equation of de Bakker and Zucker is established, presenting their solution in a conceptually simpler framework. Under an additional assumption, the equivalence between the weak equivalence relation over RSTs and the elementary equivalence relation induced by the sentences of a modal logic due to Hennessy and Milner is established.

Asynchronous multiple access tree algorithms

Random access protocols allow large numbers of low duty cycle stations to exchange messages over a shared communications channel under distributed control. Recently, a new class of random access protocols called 'tree algorithms' has emerged. Tree algorithms offer several performance advantages over other random access protocols (e.g. ALOHA and CSMA), namely higher capacity and inherently stable operation. However, only synchronous (slotted) tree algorithms have so far been defined. Any practical implementation of a synchronous protocol is complicated by the need for stations to perform the steps of the algorithm synchronously. Thus asynchronous (unslotted) protocols are of greater practical importance, especially for local networks. Here we show how to construct asynchronous versions of several well-known tree algorithms, and describe some of the performance limitations that result from asynchronous operation.

Tree encoding of speech

Recently developed methods of tree source coding with a fidelity criterion are applied to speech coding. We first demonstrate that tree codes are inherent in A-D speech convertors of the waveform following type and point to ordinary and adaptive delta modulation and differential pulse code modulation (DPCM) as examples. Insights of coding theory improve these trees at low rates; we offer two new code classes, one obtained by smoothing the DPCM tree and one using the rate-distortion theory of autoregressive sources. Using these codes, we study the performance of a simple synchronous tree searching algorithm called the M -algorithm that maintains a small fixed number of paths in contention. 1 and 2 bit/sample code trees, used to encode actual speech at 8, 10, and 16 kbits/s, yield improved dynamic range and channel error resistance, and 4-8 dB improvement in mean-square error (mse) over ordinary single-path searched DPCM. These improvements in excess of analytical estimates suggest that tree coding methods perform better with real-life sources than previously thought.