Robert M. Keller

Formal verification of parallel programs

Two formal models for parallel computation are presented: an abstract conceptual model and a parallel-program model. The former model does not distinguish between control and data states. The latter model includes the capability for the representation of an infinite set of control states by allowing there to be arbitrarily many instruction pointers (or processes) executing the program. An induction principle is presented which treats the control and data state sets on the same ground. Through the use of “place variables,” it is observed that certain correctness conditions can be expressed without enumeration of the set of all possible control states. Examples are presented in which the induction principle is used to demonstrate proofs of mutual exclusion. It is shown that assertions-oriented proof methods are special cases of the induction principle. A special case of the assertions method, which is called parallel place assertions, is shown to be incomplete. A formalization of “deadlock” is then presented. The concept of a “norm” is introduced, which yields an extension, to the deadlock problem, of Floyds technique for proving termination. Also discussed is an extension of the program model which allows each process to have its own local variables and permits shared global variables. Correctness of certain forms of implementation is also discussed. An Appendix is included which relates this work to previous work on the satisfiability of certain logical formulas.

Some approaches to best-match file searching

The problem of searching the set of keys in a file to find a key which is closest to a given query key is discussed. After “closest,” in terms of a metric on the the key space, is suitably defined, three file structures are presented together with their corresponding search algorithms, which are intended to reduce the number of comparisons required to achieve the desired result. These methods are derived using certain inequalities satisfied by metrics and by graph-theoretic concepts. Some empirical results are presented which compare the efficiency of the methods.

Towards a Theory of Universal Speed-Independent Modules

Of concern here are asynchronous modules, i.e., those whose activity is regulated by initiation and completion signals with no clocks being present. First a number of operating conditions are described that are deemed essential or useful in a system of asynchronous modules, while retaining an air of independence of particular hardware implementations as much as possible. Second, some results are presented concerning sets of modules that are universal with respect to these conditions. That is, from these sets any arbitrarily complex module may be constructed as a network. It is stipulated that such constructions be speed independent, i.e., independent of the delay time involved in any constituent modules. Furthermore it is required that the constructions be delay insensitive in the sense that an arbitrary number of delay elements may be inserted into or removed from connecting lines without effecting the external behavior of the network.

Garbage collection and task deletion in distributed applicative processing systems

The problem of automatic storage reclamation for distributed implementations of applicative languages is explored. Highly parallel distributed systems have several unique characteristics that complicate the reclamation process; in this setting, the deficiencies of existing storage reclamation schemes are thus noted. A real-time, effectively distributed, garbage collector of the mark-sweep variety, called the marking-tree collector, is shown to accomplish reclamation in parallel with the main computation, with no centralized data or control other than a logical rendezvous between phases of the collector. In addition, it is capable of finding and subsequently deleting active processes which are determined to be no longer relevant to the computation.

Look-Ahead Processors

Methods of achieving look-ahead in processing units are discussed. An optimality criterion is proposed, and several schemes are compared against the optimum under varying assumptions. These schemes include existing and proposed machine organizations, and theoretical treatments not mentioned before in this context. The problems of eliminating associative searches in the processor control and the handling of loop-forming decisions are also considered. The inherent limitations of such processors are discussed. Finally, a number of enhancements to look-ahead processors is qualitatively surveyed.

Parallel Program Schemata and Maximal Parallelism I. Fundamental Results

The phenomenon of maximal parallelism is investigated in the framework of a class of parallel program schemata. Part I presents the basic properties of this model. Two types of equivalence relation on computations are presented, to each of which there corresponds a concept of determinacy and equivalence for schemata. The correspondence between these relations is shown and related to other properties of schemata. Then the concept of maximal parallelism using one of the relations as a basis is investigated. A partial order on schemata is defined which relates their inherent parallelism. The results presented are especially concerned with schemata which are maximal with respect to this order, i.e. maximally parallel schemata. Several other properties are presented and shown to be equivalent to the property of maximal parallelism. It is then shown that for any schema of a certain class, there exists a unique equivalent schema which is maximally parallel. We call such a schema the “closure” of the original schema.

Fun and games: a new software engineering course

Computer and video games have grown to be a major industry but, until recently, have largely been ignored by academia. The last couple of years, however, have seen the emergence of new academic programs, conferences, and journals dedicated to games studies. For the past three years we have used computer games as projects in our introductory software engineering course. Small teams of students build three games across the semester. In this paper we describe the course and discuss its success.

Applicative caching

The “referential transparency” principle of applicative language expressions stipulates that a single value exists for all occurrences of an expression in a given context (where a context is a set of bindings of variables to values). In principle, each such value therefore need to be computed only once. However, in applicative language systems supporting recursive programming or tasking notions, the bindings are not all precomputed and explicit. As a result, textual recognition of all multipleoccurrences is precluded, with the unfortunate consequence that such occurrences are recomputed. We elaborate upon the early notion of “memo function” for solving this problem. We suggest syntactic and semantic constructs providing programmer control for avoiding recomputation, which is incorporated into a “building-block” approach.

Enabling computer decisions based on EEG input

Multilayer neural networks were successfully trained to classify segments of 12-channel electroencephalogram (EEG) data into one of five classes corresponding to five cognitive tasks performed by a subject. Independent component analysis (ICA) was used to segregate obvious artifact EEG components from other sources, and a frequency-band representation was used to represent the sources computed by ICA. Examples of results include an 85% accuracy rate on differentiation between two tasks, using a segment of EEG only 0.05 s long and a 95% accuracy rate using a 0.5-s-long segment.

Semantics of Networks Containing Indeterminate Operators

We discuss a denotational semantics for networks containing indeterminate operators. Our approach is based on modelling a network by the set of all its possible behaviors. Our notion of behavior is a sequence of computational actions. The primitive computational action is an event: the appearance or consumption of a token on a data path. A sequence of such events is called a history and a set of such histories is called an archive. We give composition rules that allow us to derive an archive for a network from the archive of its constituents. Causal and operational constraints on network behavior are encoded into the definitions of archives. We give a construction that allows us to obtain the denotation of networks containing loops by a process of successive approximations. This construction is not carried out in the traditional domain-theoretic setting, but rather resembles the category theoretic notion of limit. By using this construction, we avoid having to impose any closure conditions on the set of behaviors, as are typically necessary in powerdomain constructions. The resulting theory is general and compositional, but is also close to operational ideas making it a useful and flexible tool for modelling systems.