Extensive Notation Research Articles

Granular hierarchical structures of finite naïve subsets and multisets based on free monoids and homomorphisms

In this paper, we present granular hierarchical structures in which finite naive subsets and multisets are formulated by means of free monoids and homomorphisms. Our motivation is the observation that we actually write a finite subset as a finite sequence, i.e., string, in the well–known extensive notation. Such correspondence from subsets to strings, however, is not one–to–one because the concept of subsets care neither order nor repetition of their elements. The reason is nothing but a straight consequence from the axiom of extensionality. Then we must represent subsets as equivalence classes of strings with respect to some appropriate equivalence relation based on a homomorphism. Then multisets are also similarly considered as we have granular hierarchal structures of 'strings–multisets–naive subsets'. It should be noted that these formulations only require the numbers how many times each element occurs in every string. Finally the approach is shown to be able to describe every operations of finite subsets and multisets in the level of strings.

Input-output Conformance Testing for Channel-based Service Connectors

Service-based systems are software systems composed of autonomous components or services provided by different vendors, deployed on remote machines and accessible through the web. One of the challenges of modern software engineering is to ensure that such a system behaves as intended by its designer. The Reo coordination language is an extensible notation for formal modeling and execution of service compositions. Services that have no prior knowledge about each other communicate through advanced channel connectors which guarantee that each participant, service or client, receives the right data at the right time. Each channel is a binary relation that imposes synchronization and data constraints on input and output messages. Furthermore, channels are composed together to realize arbitrarily complex behavioral protocols. During this process, a designer may introduce errors into the connector model or the code for their execution, and thus affect the behavior of a composed service. In this paper, we present an approach for model-based testing of coordination protocols designed in Reo. Our approach is based on the input-output conformance (ioco) testing theory and exploits the mapping of automata-based semantic models for Reo to equivalent process algebra specifications.

Propositional Logic Constraint Patterns and Their Use in UML-Based Conceptual Modeling and Analysis

An important conceptual modeling activity in the development of database, object-oriented and agent-oriented systems is the capture and expression of domain constraints governing underlying data and object states. UML is increasingly used for capturing conceptual models, as it supports conceptual modeling of arbitrary domains, and has extensible notation allowing capture of invariant constraints both in the class diagram notation and in the separately denoted OCL syntax. However, a need exists for increased formalism in constraint capture that does not sacrifice ease of use for the analyst. In this paper, we codify a set of invariant patterns formalized for capturing a rich category of propositional constraints on class diagrams. We use tools of Boolean logic to set out the distinction between these patterns, applying them in modeling by way of example. We use graph notation to systematically uncover constraints hidden in the diagrams. We present data collected from applications across different domains, supporting the importance of "pattern-finding" for n-variable propositional constraints using general graph theoretic methods. This approach enriches UML-based conceptual modeling for greater completeness, consistency, and correctness by formalizing the syntax and semantics of these constraint patterns, which has not been done in a comprehensive manner before now

Private Friendship and Political Harmony?

Private Friendship and Political Harmony? Doron Ben-Atar (bio) James Morton Smith, ed. The Republic of Letters: The Correspondence Between Jefferson and Madison, 1776–1826, 3 vols. New York: Norton, 1995. xvii + 2073 pp. Figures, notes, bibliographical essay, and index. $150.00. Lance Banning. Jefferson and Madison: Three Conversations from the Founding. Madison: Madison House, 1995. xiii + 241 pp. Notes and index. $27.95. Revolutionaries are seldom modest. It takes a certain self-righteousness and arrogance to replace an existing order. Revolutionaries often see their struggle in millennial terms and assign it meaning and significance far beyond their time and place. A skirmish in a New England village becomes a shot heard around the world. An uprising on the periphery of the British empire is hailed as “the birthday of a new world.” An event in a specific time and place is charged with “laying the foundations of happiness for countless millions” and for “Generations yet unborn.” 1 Taking the Revolutionary generation at their word, historians frequently assign relevance and universal meaning to the American Revolution. Gordon Wood’s Pulitzer Prize-wining The Radicalism of the American Revolution, for example, proclaimed it the mother of modern democracy and capitalism. Similarly, Lance Banning and James Morton Smith believe in the relevance and timelessness of our revolutionary legacy. Banning urges us to consider “important precedents from our beginnings” (p. 47) when we approach contemporary problems — from the national debt to the widespread alienation of Americans from the political process. His elegant and stimulating narrative is followed by reprints of Jefferson and Madison’s best known statements so readers can “probe” and “learn” (p. xii) more from the Founders’ own words. Smith believes that the American founding, epitomized by Jefferson’s Declaration of Independence and Madison’s Constitution, have become the battle cry of freedom from the New World to Eastern Europe and China. In another passage he writes of “the awesome responsibility that the American people have shouldered when they ratified the Constitution. For the first time in history, an entire people had ordained, established, and ratified an organic law, [End Page 8] creating a new federal government for a new nation” (p. 591, emphasis added). Both works, though very different, focus on the collaboration between the two giants of the American republican tradition, Thomas Jefferson and James Madison. Smith and Banning emphasize the similarities between Jefferson and Madison. Both try to reach out to a wider, less scholarly, public. Banning addresses his Merrill Jensen lectures, collected as Jefferson and Madison: Three Conversations from the Founding, to “Americans who may know less about the era” and not “to scholars” (p. xi). Smith has collected and edited the nearly 1,250 letters Madison and Jefferson wrote each other. Published by a commercial press and handsomely packaged, they would look perfect on a shelf in a prestigious law office or an upper-west-side apartment. Scholarly appearance aside, these volumes target a broader audience. The Norton edition, unlike the Jefferson and Madison papers, does not indicate the source of the documents. The volumes are divided chronologically into fifty chapters, each of which is introduced by a concise essay on the relevant political history to provide historical context for nonspecialists. Smith’s impressive scholarly command of the literature comes through in the essays and extensive notation in which he directs readers to other relevant interpretations. Approaching the history of the early republic through the prism of the great collaboration, however, skews the historical record in two ways. First, Smith reads the Jefferson-Madison cooperation back into the early days of the Revolution. The letters from Governor Jefferson and Virginia’s executive council are entitled “Jefferson, Madison, and the Executive Council to....” The correspondence between Jefferson and Virginia’s congressional delegation is introduced as “Governor Jefferson to Madison and the Virginia Congressional Delegation.” Young Madison, however, was simply a member of the council and of Virginia’s congressional delegation and not the dominant member at that. The focus here on the Jefferson-Madison axis exaggerates the centrality of their collaboration to the Revolutionary struggle. Second, following in the footsteps of Julian P. Boyd’s introductory essays in the Jefferson papers, Smith toes the Jefferson industry’s...

Mormon as Editor: A Study in Colophons, Headers, and Source Indicators

Abstract The Book of Mormon contains various colophons and source indicators that signal documents or authors that Mormon and the writers of the small plates used, quoted, paraphrased, or summarized in composing the final text. Some of these headers have been italicized and separated out by the printer; others form an integral part of the text but could as well have been separated and italicized. Mormon’s extensive notation of sources is another set of evidence for the intricate and complex nature of the text and, simultaneously, of the magnitude of Mormon’s work as an ancient editor and historian.

Properties of serial kanban systems

In this paper we show some structural results of a kanban system by using results about the underlying GSMP. The main results from this connection are: dominance of allocations, optimal partition, upper and lower bounds on throughput, consistency of the IPA derivative, convexity of throughput as a function of service time parameters and concavity of throughput with respect to number of kanbans. Although the dominance and the partition results were obtained previously by sample path arguments, the proofs here are less cumbersome and generalize the earlier results. The second-order properties for kanban lines are new. These results form a basis for results in multi-product lines where proofs by sample paths require extensive notation.