In earlier work, the Abstract State Machine Thesis -- that arbitrary algorithms are behaviorally equivalent to abstract state machines -- was established for several classes of algorithms, including ordinary, interactive, small-step algorithms. This was accomplished on the basis of axiomatizations of these classes of algorithms. Here we extend the axiomatization and, in a companion paper, the proof, to cover interactive small-step algorithms that are not necessarily ordinary. This means that the algorithms (1) can complete a step without necessarily waiting for replies to all queries from that step and (2) can use not only the environment's replies but also the order in which the replies were received.
Thus @cite_27 sets modeling interaction as its goal. Different forms of interaction, such as message-passing, database queries, remote procedure calls, inputs, outputs, signals, all reduce to a single universal form: a single-reply zero-or-more-arguments not-necessarily-blocking . All arguments and the reply (if any) should be elements of the state if they are to make sense to the algorithm. For a formal definition of queries see @cite_27 ; a reminder is given in the next section. For a detailed discussion and arguments for the universality of the query-reply approach see @cite_27 .
@cite_27
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ABSTRACT This paper concerns the semantics of Codd's relational model of data. Formulated are precise conditions that should be satisfied in a semantically meaningful extension of the usual relational operators, such as projection, selection, union, and join, from operators on relations to operators on tables with “null values” of various kinds allowed. These conditions require that the system be safe in the sense that no incorrect conclusion is derivable by using a specified subset Ω of the relational operators; and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in Ω are in fact derivable in this system. Two such systems of practical interest are shown. The first, based on the usual Codd's null values, supports projection and selection. The second, based on many different (“marked”) null values or variables allowed to appear in a table, is shown to correctly support projection, positive selection (with no negation occurring in the selection condition), union, and renaming of attributes, which allows for processing arbitrary conjunctive queries. A very desirable property enjoyed by this system is that all relational operators on tables are performed in exactly the same way as in the case of the usual relations. A third system, mainly of theoretical interest, supporting projection, selection, union, join, and renaming, is also discussed. Under a so-called closed world assumption, it can also handle the operator of difference. It is based on a device called a conditional table and is crucial to the proof of the correctness of the second system. All systems considered allow for relational expressions containing arbitrarily many different relation symbols, and no form of the universal relation assumption is required. Categories and Subject Descriptors: H.2.3 [Database Management]: Languages— query languages; H.2.4 [Database Management]: Systems— query processing General Terms: Theory This paper is concerned with protection of information in relational databases from disclosure to properly identified users. It is assumed that the only means of access to the database is through a relational query language. The objective of the paper is to formalize the notion of protection. We first describe the information content of the database by a set of propositions and their truth values. The objects to be protected are (the truth values of) certain propositions that have been declared confidential. A query violates a protected proposition if its answer modifies the knowledge of tHe user about (the truth value of) this proposition. Following this approach, we propose a model for evaluating protection systems. In this model a protection system is characterized by the type of queries it takes as its input, the type of data it can protect, the means of protection against queries (e.g. rejection or modification) and the type of protection it provides (e.g., total protection, partial protection, protection against user's inference). Some examples of the use of the model as a tool for analysis are given. We critically evaluate the current state of research in multiple query opGrnization, synthesize the requirements for a modular opCrnizer, and propose an architecture. Our objective is to facilitate future research by providing modular subproblems and a good general-purpose data structure. In rhe context of this archiuzcture. we provide an improved subsumption algorithm. and discuss migration paths from single-query to multiple-query oplimizers. The architecture has three key ingredients. First. each type of work is performed at an appropriate level of abstraction. Segond, a uniform and very compact representation stores all candidate strategies. Finally, search is handled as a discrete optimization problem separable horn the query processing tasks. 1. Problem Definition and Objectives A multiple query optimizer (h4QO) takes several queries as input and seeks to generate a good multi-strategy, an executable operator gaph that simultaneously computes answers to all the queries. The idea is to save by evaluating common subexpressions only once. The commonalities to be exploited include identical selections and joins, predicates that subsume other predicates, and also costly physical operators such as relation scans and SOULS. The multiple query optimization problem is to find a multi-strategy that minimizes the total cost (with overlap exploited). Figure 1 .l shows a multi-strategy generated exploiting commonalities among queries Ql-Q3 at both the logical and physical level. To be really satisfactory, a multi-query optimization algorithm must offer solution quality, ejjiciency, and ease of Permission to copy without fee all a part of this mataial is granted provided that the copies are nut made a diitributed for direct commercial advantage, the VIDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Da Blse Endowment. To copy otherwise. urturepublim identify many kinds of commonalities (e.g., by predicate splitting, sharing relation scans); and search effectively to choose a good combination of l-strategies. Efficiency requires that the optimization avoid a combinatorial explosion of possibilities, and that within those it considers, redundant work on common subexpressions be minimized. ‘Finally, ease of implementation is crucial an algorithm will be practically useful only if it is conceptually simple, easy to attach to an optimizer, and requires relatively little additional soft- We consider the model of population protocols introduced by (Computation in networks of passively mobile finite-state sensors, pp. 290–299. ACM, New York, 2004), in which anonymous finite-state agents stably compute a predicate of the multiset of their inputs via two-way interactions in the family of all-pairs communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of two-way interaction, we also consider several variants of the model in which agents communicate by anonymous message-passing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These one-way models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these one-way models using natural subclasses of the semilinear predicates.