W. Richard Stark

Automatic model construction

An algorithm for the construction of finite models of sets of predicate-calculus sentences is given. The algorithm differs from resolution in its ability to incorporate certain extra sentences (human advice) gracefully. Since the problem attacked by the algorithm is NP-complete, it is hoped that this ability to accept advice will make the algorithm useful more as a tool in the hands of a researcher than as a stand-alone procedure.

A Logic of Knowledge

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Amorphous computing: examples, mathematics and theory

The cellular automata model was described by John von Neumann and his friends in the 1950s as a representation of information processing in multicellular tissue. With crystalline arrays of cells and synchronous activity, it missed the mark (Stark and Hughes, BioSystems 55:107–117, 2000). Recently, amorphous computing, a valid model for morphogenesis in multicellular information processing, has begun to fill the void. Through simple examples and elementary mathematics, this paper begins a computation theory for this important new direction.

Homeostasis in synchronous distributed computation, a formal view

Abstract Our objective is to introduce and illustrate a few basic notions upon which a mathematics of distributed computation can begin to develop. The central issue, as we see it, concerns the existence of a distributed, locally determined, global dynamics which responds homeostatically to a changing environment. This paper contains two elementary examples of such systems expressed in terms of our basic notions. A simple theorem characterizing the existence of such systems in a special case is proved. The theorem, the examples, and the associated discussion demonstrate the utility of our formalism.

DYNAMICS FOR A FUNDAMENTAL PROBLEM OF BIOLOGICAL INFORMATION PROCESSING

This paper presents results on the dynamics of asynchronous irregular cellular automata (as representations of natural information-processing systems). It is an approach to explaining global dynamics from local dynamics without the use of unrealistic intermediate structure (i.e., without synchronization or regular communication). The unrealistic intermediate structure is replaced by the the realistic assumption that local behavior is entropy reducing (an idea of E. Schrodinger). It has been shown that, for systems composed of cells programmed as cyclic finite-state automata, the observed global oscillation can be explained in terms of the structure of attractors in the global state space. The degree of local connectivity (i.e., of communication between cells) is shown here to determine the size of global attractors, and in turn the sharpness of global behavior. However, the primary result here is the extension of these results to systems whose cells are programmed as arbitrary strongly connected automata. Finally, these phenomena are demonstrated by the simulations.

The social metaphor for distributed processing

Abstract Social systems are asynchronous distributed processors characterized by (i) a large and variable population of small individuals and (ii) a random and changing communications architecture. Individual interactions produce global computations or processes which are immune to minor structural changes. Termite colonies are a good example. Global processes—such as the construction of a mound—are essentially unaffected by most details of colony structure. How are global computations programmed locally? What types of programs are immune to structural changes? Given the ability to program at the individual level, can social systems be viewed as general purpose computers? These and similar questions have motivated this paper. We present (i) precise definitions for social systems and related concepts, (ii) seven programs resulting in interesting global processes, (iii) theorems describing the effect of structural changes on various global processes, and (iv) some questions for further research.

Random choice in amorphous processes

I prove that the natural multicellular environment requires random scheduling of cell activity in order to successfully execute arbitrary amorphous programs. This proof uses an unusual new method of constructing amorphous programs. Amorphous processes model natural multicellular information processing and so it is finite in most respects. Thus it is surprising that a non-computable operation (random choice for cell activity) is an essential part of the formalism’s interpretation. The necessary randomness could originate in thermodynamic events. To the extent that amorphous processes successfully model multicellular biological information processing, this result suggests that there is something essential to the processes of life and evolution that lies just beyond Turing computability.

On the complexity of deadlock-free programs on a ring of processors

Abstract A combinatorial view of deadlock (as in Dijkstras self-stabilizing systems) is presented which leads to precise lower bounds on the complexity of programs. Specifically, we consider a directed ring of k individual processors, each having n states, identical programs, and asynchronous activity. Our main theorem establishes the minimum size (i.e., complexity) of a program for which no global state is in deadlock.

Tissue models, with programming problems from God's notebook.

The individual cells within a multicellular organism do not operate autonomously but instead interact together in a controlled and co-ordinated manner. In order that an organism can function ... there must be some form of communication between the component cells. ... [It] may take the form of direct communication between adjacent cells ... through permeable membrane channels known as gap junctions. MacDonald [Ma85].

Automatic Reasoning, Algebraic Intelligence

What is really happening when a machine does something that seems to be intelligent? If it recognizes a spoken word, proves a theorem, plays a good chess game, or solves a problem in calculus, then does it have some idea of what is going on? Of course not. Machine intelligence is fundamentally different from human intelligence. It is an illusion based on algebraic links between syntax and semantics. The semantics of a language represents meaning in terms of an object world. When a machine’s behavior seems intelligent, it is because it is semantically appropriate. However, the machine is simply a symbol shuffler—its abilities are limited to syntactic processing. Algebraic systems which provide strong formal connections between their semantics and their syntax make it possible for a symbol shuffling machine to appear to understand what it is doing.