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On the algebraic variance of linear transformations and its applications to algebraic codes
Abstracts
both the above-mentioned ones, due to the smaller number of partial products, or to the smaller number of partial-product bits. Addition cells of the proposed multiplier array are composed of pairs of one-bit full adders. These two-adder cells can be treated as redundant onedigit adders for the digits 0, 1, 2, or - 1 , 0, ÷ 1, encoded by the bit-pairs 00, 01, 10, 11. Such cells are more advantageous than redundant adders fr the digits - 1 , 0, 4-1, encoded by the bit pairs 10, 00, 01 only. Author's Abstract
Shlomo Moran: On the Cost of Reducing the Interaction in Interactive Proof Protocols, Department of Computer Science, Israel lstitute of Technology, Haifa, Nov. 1986. The following problem is considered: Let L be a language that can be accepted by an interactive proof protocol with f(n)-time bounded verifier within g(n) interactions. How powerful, in terms of time complexity, must be a verifier that accepts L by an interactive proof protocol with only one interaction? A pure complexity-theoretic argument implies an that a 2°c/~n'-time bounded verifier is always sufficiently powerful (independent on the number of interactions, g(n)). This bound was improved for slowly increasing g ( n ) b y the results of [B] and [GS', which implies that a f(n)°¢2s'"')time bounded verifier can accept L within one interaction. The main result of this paper improves that last upper bound to f(n) gcn)°°). Another application of that result is that the number of interactions needed to recognize a language by an interactive proof protocol with a polynomial time bounded verifier is invariant under multiplication by a (positive) constant. For comparison, the results of [B] and [GS] mentioned above implies only that this number is invariant under additive constant. Author's Abstract
Brian A. Nixon, K. Lawrence Chung, David Lauzon, Alex Borgida, John Myiopoulos and Martin Stanley: Implementing a Taxis Compiler, Computer Systems Research Institute, University of Toronto, Jan. 1987. The features of a compiler for the Taxis design language are described and discussed. "Iaxis offers
151
an entity-based framework for designing interactive information systems and supports generalisation, classification and aggregation as abstraction mechanisms. Its features include multiple inheritance of attributes, isA hierarchies of transactions, metaclasses, typed attributes, a procedural exception-handling mechanism, an iteration construct based on the abstraction mechanisms supported, semantic integrity constraints, including timedependent ones, and communicating Petri net-like processes (called scripts). Developing a compiler for the language involved tackling the problem of efficiently representing and accessing a large collection of entities, performing (static) type checking and representing isA hierarchies of transactions. The compiler has also been designed to deal with semantic integrity constraints and scripts, though these features have not yet been implemented. Authors' Abstract
Werner Pohlmann: Simulierte Zeit und das Ada Rendezvous, Institut fuer lnformatik, Technische Universitaet Muenchen, Nov. 1986. 'Simulated time and the Ada rendezvous'. Choosing Ada as a base language for the process view of simulation, one would Like to adopt the Ada rendezvous for process interaction. This paper investigates the implications of the rendezvous in the context of simulated time. To avoid the danger of deadlock (as exhibited by some proposed systems), a very thorough control of the rendezvous is shown to be necessary. A suitable simulation mechanism is presented and proven. But judged by the ensuing costs the rendezvous is considered to be no attractive choice for general simulation purposes. Considering methods, this paper uses and con° tributes to the 'space-time view' (L. Lamport) of processes: processes are sequences of actions, and simulated time is a mapping of actions to numerical values. Author's Abstract R.M. Roth and A. Lempei: On the Algebraic Variance of Linear Transformations and its Applications to Algebraic Codes, Department of Com-
152
Abstracts
puter Science, Israel Institute of Technology, Haifa, Sept. 1986. Let F be a field, let ~: F k ~ F k be a nonsingular linear transformation over F, and let polynomials of degree k - 1, or less, over F be represented by the k-vector of their coefficients. The root variance O(u) of the polynomial u is defined as the number of distinct root of u in F. The algebraic variance p(~, k) of p is defined as the maximum over all u ¢ F k - {0} of the sum p(u) + p(~(u)). In this paper we investigate the existence of transformations ~ such that p(~, k ) < 2 ( k - 1), with emphasis on finite fields, where the existence of such transformations leads to the construction of good long algebraic codes. For the first interesting case of k = 3, it is shown that over the complex field, or over any subfield of the real field, or over any finite field with more than seven elements, the algebraic variance of every linear transformation equals to 4.
employment the total amount is quite low. Earnings from those activities are hardly more than one p.c. of the GNP. - Although receiving unemployment compensation is often accompanied by work in the underground economy, this cannot be taken for usual behavior. In fact, unemployed persons are comperatively more active in secondary employment (17.6 p.c.) than the average (9.6 p.c.). Nevertheless only one out of ten recipients of unemployment compensation is engaged in secondary employment. - Regulations and institutions are important factors to determinate the extent of underground economy. Author's Abstract
Josef Winkowski: Towards an algebraic model for communicating processes, Institute of Computer Science, Polish Academy of Sciences, Warsaw December 1986.
Author's Abstract
Johannes Schwarze: Umfang des schattenwirtsehafllichen Arbeitsangebotes in der Nebenerwerbstaetigkeit, Sonderforschungsbereich 3, J.W. Goethe-Universitaet Frankfurt und Universitaet Mannheim, Dezember 1987. This paper deals with the extension of under° ground economy in secondary employment. Secondary employment activities are more appropriate for concealment than activities in the main job. Proceeding on a representative survey of secondary employment, the regulation of the 'Gesetz zur Bek~mpfung der Schwarzarbeit' and the regulation of the social security system will be simulated. This allows the determination of the potential undergound labor force. The main findings are: - Defining underground employment by the two criteria mentioned above leads to the result that almost 40 p.c. of secondary employment (about 1.5 Mill. persons) can be considered underground labor force. It is quite sure, that this quota will increase significantly if the criteria 'tax defraud' is added. - In contrast to the comperatively frequent occurence of underground economy in secondary
A new semantics for communicating processes is introduced which modifies the ideas of Milner (1980) and Winskel (1982 and 1983). This semantics avoids representing hidden events of processes and it offers conceptual means to cope with indivisible complexes of events. Author's Abstract
Klaus Wolff: Schattenwirtschaft - Micro- und Makrooekonomische Ergebnisse fuer die Bundesrepublik Deutschland, Sonderforschungsbereich 3, J.W. Goethe-Universitaet mad Universitaet Mannhelm, Jan. 1987. This paper presents an overview of existing estimates concerning the underground economy in the Federal Republic of Germany. Besides macroeconomic approaches to the problem and their appraisals, the focus is on the estimates conducted in West Germany on the micro level. In this context, first own results concerning the limits of potential underground work are presented on the basis of current data from the Sfb3-Secondary Occupation Survey 1984. Author's Abstract
both the above-mentioned ones, due to the smaller number of partial products, or to the smaller number of partial-product bits. Addition cells of the proposed multiplier array are composed of pairs of one-bit full adders. These two-adder cells can be treated as redundant onedigit adders for the digits 0, 1, 2, or - 1 , 0, ÷ 1, encoded by the bit-pairs 00, 01, 10, 11. Such cells are more advantageous than redundant adders fr the digits - 1 , 0, 4-1, encoded by the bit pairs 10, 00, 01 only. Author's Abstract
Shlomo Moran: On the Cost of Reducing the Interaction in Interactive Proof Protocols, Department of Computer Science, Israel lstitute of Technology, Haifa, Nov. 1986. The following problem is considered: Let L be a language that can be accepted by an interactive proof protocol with f(n)-time bounded verifier within g(n) interactions. How powerful, in terms of time complexity, must be a verifier that accepts L by an interactive proof protocol with only one interaction? A pure complexity-theoretic argument implies an that a 2°c/~n'-time bounded verifier is always sufficiently powerful (independent on the number of interactions, g(n)). This bound was improved for slowly increasing g ( n ) b y the results of [B] and [GS', which implies that a f(n)°¢2s'"')time bounded verifier can accept L within one interaction. The main result of this paper improves that last upper bound to f(n) gcn)°°). Another application of that result is that the number of interactions needed to recognize a language by an interactive proof protocol with a polynomial time bounded verifier is invariant under multiplication by a (positive) constant. For comparison, the results of [B] and [GS] mentioned above implies only that this number is invariant under additive constant. Author's Abstract
Brian A. Nixon, K. Lawrence Chung, David Lauzon, Alex Borgida, John Myiopoulos and Martin Stanley: Implementing a Taxis Compiler, Computer Systems Research Institute, University of Toronto, Jan. 1987. The features of a compiler for the Taxis design language are described and discussed. "Iaxis offers
151
an entity-based framework for designing interactive information systems and supports generalisation, classification and aggregation as abstraction mechanisms. Its features include multiple inheritance of attributes, isA hierarchies of transactions, metaclasses, typed attributes, a procedural exception-handling mechanism, an iteration construct based on the abstraction mechanisms supported, semantic integrity constraints, including timedependent ones, and communicating Petri net-like processes (called scripts). Developing a compiler for the language involved tackling the problem of efficiently representing and accessing a large collection of entities, performing (static) type checking and representing isA hierarchies of transactions. The compiler has also been designed to deal with semantic integrity constraints and scripts, though these features have not yet been implemented. Authors' Abstract
Werner Pohlmann: Simulierte Zeit und das Ada Rendezvous, Institut fuer lnformatik, Technische Universitaet Muenchen, Nov. 1986. 'Simulated time and the Ada rendezvous'. Choosing Ada as a base language for the process view of simulation, one would Like to adopt the Ada rendezvous for process interaction. This paper investigates the implications of the rendezvous in the context of simulated time. To avoid the danger of deadlock (as exhibited by some proposed systems), a very thorough control of the rendezvous is shown to be necessary. A suitable simulation mechanism is presented and proven. But judged by the ensuing costs the rendezvous is considered to be no attractive choice for general simulation purposes. Considering methods, this paper uses and con° tributes to the 'space-time view' (L. Lamport) of processes: processes are sequences of actions, and simulated time is a mapping of actions to numerical values. Author's Abstract R.M. Roth and A. Lempei: On the Algebraic Variance of Linear Transformations and its Applications to Algebraic Codes, Department of Com-
152
Abstracts
puter Science, Israel Institute of Technology, Haifa, Sept. 1986. Let F be a field, let ~: F k ~ F k be a nonsingular linear transformation over F, and let polynomials of degree k - 1, or less, over F be represented by the k-vector of their coefficients. The root variance O(u) of the polynomial u is defined as the number of distinct root of u in F. The algebraic variance p(~, k) of p is defined as the maximum over all u ¢ F k - {0} of the sum p(u) + p(~(u)). In this paper we investigate the existence of transformations ~ such that p(~, k ) < 2 ( k - 1), with emphasis on finite fields, where the existence of such transformations leads to the construction of good long algebraic codes. For the first interesting case of k = 3, it is shown that over the complex field, or over any subfield of the real field, or over any finite field with more than seven elements, the algebraic variance of every linear transformation equals to 4.
employment the total amount is quite low. Earnings from those activities are hardly more than one p.c. of the GNP. - Although receiving unemployment compensation is often accompanied by work in the underground economy, this cannot be taken for usual behavior. In fact, unemployed persons are comperatively more active in secondary employment (17.6 p.c.) than the average (9.6 p.c.). Nevertheless only one out of ten recipients of unemployment compensation is engaged in secondary employment. - Regulations and institutions are important factors to determinate the extent of underground economy. Author's Abstract
Josef Winkowski: Towards an algebraic model for communicating processes, Institute of Computer Science, Polish Academy of Sciences, Warsaw December 1986.
Author's Abstract
Johannes Schwarze: Umfang des schattenwirtsehafllichen Arbeitsangebotes in der Nebenerwerbstaetigkeit, Sonderforschungsbereich 3, J.W. Goethe-Universitaet Frankfurt und Universitaet Mannheim, Dezember 1987. This paper deals with the extension of under° ground economy in secondary employment. Secondary employment activities are more appropriate for concealment than activities in the main job. Proceeding on a representative survey of secondary employment, the regulation of the 'Gesetz zur Bek~mpfung der Schwarzarbeit' and the regulation of the social security system will be simulated. This allows the determination of the potential undergound labor force. The main findings are: - Defining underground employment by the two criteria mentioned above leads to the result that almost 40 p.c. of secondary employment (about 1.5 Mill. persons) can be considered underground labor force. It is quite sure, that this quota will increase significantly if the criteria 'tax defraud' is added. - In contrast to the comperatively frequent occurence of underground economy in secondary
A new semantics for communicating processes is introduced which modifies the ideas of Milner (1980) and Winskel (1982 and 1983). This semantics avoids representing hidden events of processes and it offers conceptual means to cope with indivisible complexes of events. Author's Abstract
Klaus Wolff: Schattenwirtschaft - Micro- und Makrooekonomische Ergebnisse fuer die Bundesrepublik Deutschland, Sonderforschungsbereich 3, J.W. Goethe-Universitaet mad Universitaet Mannhelm, Jan. 1987. This paper presents an overview of existing estimates concerning the underground economy in the Federal Republic of Germany. Besides macroeconomic approaches to the problem and their appraisals, the focus is on the estimates conducted in West Germany on the micro level. In this context, first own results concerning the limits of potential underground work are presented on the basis of current data from the Sfb3-Secondary Occupation Survey 1984. Author's Abstract