A New Implementation of Automath

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features: It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds. Its implementation of -terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder. The program can compile an Automath text into one big Automath single line-style -term. It outputs such a term using de Bruijn indices. (These -terms cannot be checked by modern systems like Coq or Agda, because the -typed -calculi of de Bruijn are different from the -typed -calculi of modern type theory.)The source of aut is freely available on the Web at the address .     

Logic Based Abstractions of Real-Time Systems

When verifying concurrent systems described by transition systems, state explosion is one of the most serious problems. If quantitative temporal information (expressed by clock ticks) is considered, state explosion is even more serious. We present a notion of abstraction of transition systems, where the abstraction is driven by the formulae of a quantitative temporal logic, called qu-mu-calculus, defined in the paper. The abstraction is based on a notion of bisimulation equivalence, called , n-equivalence, where is a set of actions and n is a natural number. It is proved that two transition systems are , n-equivalent iff they give the same truth value to all qu-mu-calculus formulae such that the actions occurring in the modal operators are contained in , and with time constraints whose values are less than or equal to n. We present a non-standard (abstract) semantics for a timed process algebra able to produce reduced transition systems for checking formulae. The abstract semantics, parametric with respect to a set of actions and a natural number n, produces a reduced transition system , n-equivalent to the standard one. A transformational method is also defined, by means of which it is possible to syntactically transform a program into a smaller one, still preserving , n-equivalence.     

The Objective Conception of Context and Its Logic

In this paper, an objective conception of contexts based loosely upon situation theory is developed and formalized. Unlike subjective conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended first-order language for this account is developed. The language contains complex terms for propositions, and the standard predicate ist that expresses the relation that holds between a context and a proposition just in case the latter is true in the former. The logic for the objective conception features a global classical predicate calculus, a local logic for reasoning within contexts, and axioms for propositions. The specter of paradox is banished from the logic by allowing ist to be nonbivalent in problematic cases: it is not in general the case, for any context c and proposition p, that either ist(c,p) or ist(c, ¬ p). An important representational capability of the logic is illustrated by proving an appropriately modified version of an illustrative theorem from McCarthy's classic Blocks World example.     

Decision procedures for elementary sublanguages of set theory: X. Multilevel syllogistic extended by the singleton and powerset operators

The class of unquantified formulae of set theory involving Boolean operators, the powerset and singleton operators, and the equality and membership predicates is shown to have a solvable satisfiability problem.It is shown that whenever a formula in the above class is satisfiable there exists a hereditarily finite model of , whose rank is bounded by a doubly exponential expression in the number of variables occurring in .This paper was written while the author was a Visiting Professor at Courant Institute of Mathematical Sciences, New York University, U.S.A.     

Where does the end begin? Problems in musico-cognitive modeling

Research with computer systems and musical grammars into improvisation as found in the tabla drumming system of North India has indicated that certain musical sentences comprise (a) variable prefixes, and (b) fixed suffixes (or cadences) identical with those of their original rhythmic themes. It was assumed that the cadence functioned as a kind of target in linear musical space, and yet experiments showed that defining what exactly constituted the cadence was problematic. This paper addresses the problem of the status of cadential patterns, and demonstrates the need for a better understanding and formalization of ambiguity in musico-cognitive processing. It would appear from the discussion that the cadence is not a discrete unit in itself, but just part of an ever-present underlying framework comprising the entire original rhythmic theme. Improvisations (variations), it is suggested, merely break away from and rejoin this framework at important structural points. This endorses the theory of simultaneity. However, the general cognitive implications are still unclear, and further research is required to explore musical ambiguity and the interaction of musical, linguistic, and spatio-motor grammars.     

Data encodings and their costs

Summary This paper is devoted to developing and studying a precise notion of the encoding of a logical data structure in a physical storage structure, that is motivated by considerations of computational efficiency. The development builds upon the notion of an encoding of one graph in another. The cost of such an encoding is then defined so as to reflect the structural compatibility of the two graphs, the (externally specified) costs of implementing the host graph, and the (externally specified) set of intended usage patterns of the guest graph. The stability of the constructed framework is demonstrated in terms of a number of results; the faithfulness of the formalism is argued in terms of a number of examples from the literature; and the tractability of the model is hinted at by several results and by further references to the literature.     

The Origins of the Translator's Workstation

The first proposals for various component tools of what is now called the translator's workstation or translator's workbench are traced back to the 1970s and early 1980s in various, often independent, proposals at different stages in the development of computers and in their use by translators.     

A formal model of atomicity in asynchronous systems

Summary We propose a generalisation of occurrence graphs as a formal model of computational structure. The model is used to define the atomic occurrence of a program, to characterise interference freeness between programs, and to model error recovery in a decentralised system.     

Complexity and computability of solutions to linear programming systems

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal centered-cutoff algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By model approximation, both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral constraint contraction algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the imposed problem ignorance of past complexity research is deleterious to research progress on computability or efficiency of computation.This research was partly supported by Project NR047-071, ONR Contract N00014-80-C-0242, and Project NR047-021, ONR Contract N00014-75-C-0569, with the Center for Cybernetic Studies, The University of Texas at Austin.     

An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization

We give an O(^k · n²) fixed parameter tractable algorithm for the 1-Sided Crossing Minimization. The constant in the running time is the golden ratio = (1+5)/2 1.618. The constant k is the parameter of the problem: the number of allowed edge crossings.     

Explanation-Based Learning for Diagnosis

We present explanation-based learning (EBL) methods aimed at improving the performance of diagnosis systems integrating associational and model-based components. We consider multiple-fault model-based diagnosis (MBD) systems and describe two learning architectures. One, EBLIA, is a method for learning in advance. The other, EBL(p), is a method for learning while doing. EBLIA precompiles models into associations and relies only on the associations during diagnosis. EBL(p) performs compilation during diagnosis whenever reliance on previously learned associational rules results in unsatisfactory performance—as defined by a given performance threshold p. We present results of empirical studies comparing MBD without learning versus EBLIA and EBL(p). The main conclusions are as follows. EBLIA is superior when it is feasible, but it is not feasible for large devices. EBL(p) can speed-up MBD and scale-up to larger devices in situations where perfect accuracy is not required.     

Enhancing the performance of an agent-based manufacturing system through learning and forecasting

Agent-based technology has been identified as an important approach for developing next generation manufacturing systems. One of the key techniques needed for implementing such advanced systems will be learning. This paper first discusses learning issues in agent-based manufacturing systems and reviews related approaches, then describes how to enhance the performance of an agent-based manufacturing system through learning from history (based on distributed case-based learning and reasoning) and learning from the future (through system forecasting simulation). Learning from history is used to enhance coordination capabilities by minimizing communication and processing overheads. Learning from the future is used to adjust promissory schedules through forecasting simulation, by taking into account the shop floor interactions, production and transportation time. Detailed learning and reasoning mechanisms are described and partial experimental results are presented.     

Volume functions of historical texts and the amplitude correlation principle

A new empirico-statistical model is suggested to distinguish dependent narrative texts from independent narrative texts by means of their volume functions. A regard for information principle and an amplitude correlation principle are formulated. The model and both principles are examined experimentally using specific historical texts.Anatoliy T. Fomenko (Dr. Sci. in mathematics, Lomonosov State University) is a Professor at Lomonosov State University, Moscow. He is author of twelve monographs and textbooks, and is co-author of the two-volume Modern Geometry (Springer-Verlag). He is also artist and historian.Svetlozar T. Rachev (Dr. Sci., Steklov Mathematical Institute) is a Professor at the University of California, Santa Barbara. He has published more than seventy papers and is co-author of the monographMathematical Models for Construction of Queuing Models (Moscow, 1988). His main interests are: stability of stochastic models, theory of probability metrics, queuing theory and survival models.     

Searching minimax game trees under memory space constraint

Games such as CHESS, GO and OTHELLO can be represented by minimax game trees. Among various search procedures to solve such game trees,- and SSS^* are perhaps most well known. Although it is proved that SSS^* explores only a subset of the nodes explored by-, - is commonly believed to be faster in real applications, since it requires very little memory space and hence its storage management cost is low. Contrary to this folklore, however, this paper reports, using the OTHELLO game as an example, that SSS^* is much faster than-. It is also demonstrated that SSS^* can be modified to make the required memory space controllable to some extent, while retaining the high efficiency of the original SSS^*.This research was partially supported by the Ministry of Education, Science and Culture of Japan, under a Scientific Grant-in-Aid.     

From Conditional Events to Conditional Measures: A New Axiomatic Approach

Our starting point is a definition of conditional event EH which differs from many seemingly similar ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same third value u (undetermined) to all conditional events, but make it depend on EH, it turns out that this function t(EH) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, compulsory – choice of the relevant operations among conditional events) the natural axioms for many different (besides probability) conditional measures.     

A Generalization of Jumps and Labels

This paper describes a new language feature that is a hybrid of labels and procedures. It is closely related to jumping out of a functional subroutine, and includes conventional labels and jumping as a special, but probably not most useful, case. It is independent of assignment, ie., it can be added to a purely-functional (non-imperative) system (such as LISP without pseudo-functions or program feature). Experiments in purely functional programming suggest that its main use will be in success/failure situations, and failure actions. This innovation is incorporated in the projected experimental system, ISWIM.     

Integration of 3-D shape construction and assembly to realize micro systems

In order to make micro 3-D structures, we are designing a table-sized factory, namely Nano Manufacturing World (NMW). In NMW, we challenged to use a new process fused by semiconductor process for preciseness and machine process for 3-dimensionality. In order to realize the new process, we designed three new mechanisms in this paper: multi-face shape making beam, co-focus rotational robot and micro mechanical tools. Through an evaluation to actually make a micro Gojunoto with the mechanisms, we confirmed their validities for functions of integration of 3-D shape construction and assembly.     

Machine mathematics: Problems and prospects

Pitfalls are considered that arise during the implementation of theoretically justified algorithms of computational mathematics in solving scientific and technical problems and lead to computer solutions that have no physical meaning.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 65–72, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

States and the free orthogonality monoid

Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (, ) denote the free orthogonality monoid over (X, #). Let C₀(, ) be the subset of C(, ), consisting of all closures of bounded orthogonal sets. We show that C₀(, ) is a suborthomodular lattice of C(, ) and we provide a necessary and sufficient condition for C₀(, ) to carry a full set of dispersion free states.The work of the second author on this paper was supported by National Science Foundation Grant GP-9005.     

Fuzzy probabilities for web planning

We apply our new approach to modeling uncertain probabilities to queuing theory and the optimal design of web servers. This involves using fuzzy, finite, regular Markov chains to determine the fuzzy steady state probabilities and then computing the fuzzy numbers for system performance. We first ignore revenues and costs in determining an optimal system and then we incorporate these factors for optimal design. Then we add two new phenomena associated with the web in our optimization models: burstiness and long tailed distributions.