Gyorgy Turan - Academia.edu (original) (raw)

Papers by Gyorgy Turan

Automata, Languages and Programming, 1991

... There are several lower bound results for this function in different models, using the fact t... more ... There are several lower bound results for this function in different models, using the fact that its table is an Haxiamard matrix (TarjŁn (1975), Chor and Goldreich (1985), Babai, Frankl and Simon (1986), Hajnai, Maass, Pudl~k, Szegedy and TurŁn (1987), Bruck (1990)). ...

Journal of Computer and System Sciences, 1987

We give a C" lower bound for read-once-only branching programs computing an explicit Boolean func... more We give a C" lower bound for read-once-only branching programs computing an explicit Boolean function. For n = (;), the function computes the parity of the number of triangles in a graph on v vertices. This improves previous exp(c &) lower bounds for other graph functions by Wegener and Zak. The result implies a linear lower bound for the space complexity of this Boolean function on "eraser machines," i.e., machines that erase each input bit immediately after having read it.

Information and Computation, 2022

Lower and upper bounds are given for the number of prototypes required for various nearest neighb... more Lower and upper bounds are given for the number of prototypes required for various nearest neighbor representations of Boolean functions.

Discrete Mathematics & Theoretical Computer Science, Aug 16, 2012

A formal framework is given for the characterizability of a class of belief revision operators, d... more A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a definability property of the class of partial orders in monadic second-order logic. Based on a non-definability result for a class of partial orders, an example is given of a non-characterizable class of revision operators. This appears to be the first non-characterizability result in belief revision.

We give a revision algorithm for monotone DNF formulas in the general revision model (additions a... more We give a revision algorithm for monotone DNF formulas in the general revision model (additions and deletions of variables) that uses O(m 3 e log n) queries, where m is the number of terms, e the revision distance to the target formula, and n the number of variables. We also give an algorithm for revising 2-term unate DNF formulas in the same model, with a similar query bound. Lastly, we show that the earlier query bound on revising readonce formulas in the deleti...

Fundamentals of Computation Theory, 1981

Proceedings of a Workshop on Computational Learning Theory and Natural Learning Systems Constraints and Prospects Constraints and Prospects, Aug 25, 1994

Lecture Notes in Computer Science, 1997

Lecture Notes in Computer Science, 1991

In the introduction of his paper starting computational learning theory, Valiant observed that th... more In the introduction of his paper starting computational learning theory, Valiant observed that the intuitive notion of learning merits similar attention from the point of view of formal theoretical study as that of the notion of computing. In this comparison, learning appears to be more elusive, more difficult to capture by a unified mathematical theory (as noted by Haussler (1990), it is not clear whether such a theory is even possible or desirable). Research was focused on concept learning, which is in fact closely related to computing in that several approaches developed in theoretical computer science can be adapted to its study. Interesting connections were found with other fields such as combinatorial optimization, cryptography and statistical pattern recognition. In this survey we gave a short account of some aspects of the results obtained in computational learning theory, by describing several learning models, characterizations of learnability, some learning algorithms and negative results.

Lecture Notes in Computer Science, 1991

... There are several lower bound results for this function in different models, using the fact t... more ... There are several lower bound results for this function in different models, using the fact that its table is an Haxiamard matrix (TarjŁn (1975), Chor and Goldreich (1985), Babai, Frankl and Simon (1986), Hajnai, Maass, Pudl~k, Szegedy and TurŁn (1987), Bruck (1990)). ...

Theoretical Advances in Neural Computation and Learning, 1994

Proceedings of the eleventh annual conference on Computational learning theory - COLT' 98, 1998

We consider the learnability of some concept classes in predicate logic with proper equivalence q... more We consider the learnability of some concept classes in predicate logic with proper equivalence queries. Concepts are represented by atomic formulas over a restricted language. The concept represented by an atomic formula consists of its ground instances having bounded depth. In addition, it is assumed that there is a first-order sentence given, and the COIIcept class contains only those atomic forrnulas which satisfy this sentence. For instance, one may consider the learnability of atomic formulas that represent symmetric, or transitive concepts. It is shown that every such concept class can be learned with O(m2 +m log n) queries, where m is the quantifier rank of the sentence and n is the depth bound for the ground instances. The proof uses a combination of tools from logic and learning algorithms for geometric concepts. Model theoretic games are used to determine the structure of the concept classes. We formulate a constrained version of the problem of learning two-dimensional axis-parallel rectangles, where one corner is required to belong to a prespecified subset. A sufficient condition is given for the efficient learnability of a rectangle in terms of the geometric properties of this subset. The algorithm for the predicate logic learning problem is obtained by combining the learning algorithm for the constrained rectangle learning problem with the informa*Current affiliation: Investment Technologies International, Chicago, IL. +Artificial Intelligence Research Croup of the Hungarian Academy of Sciences, Szeged, Hungary. Partially supported by grmts ESPRIT 20237 and OTKA T-016349 Permission to make digital or hard copies ofall or part ofthis work for personal or chxssroom use is granted without fee provided that copies are not made or distributed for prolit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to rrpuhlish, IO post on servers or to redistribute to lists, requires prior spccikic permission and/or a fee. COLT 98 Madison WI USA Copyright ACM 1998 I-581 13-057--O/98/ 7...$5.00 Gyiirgy Tur6n t Department of MSCS University of Illinois at Chicago 851 S.Morgan, M/C 249 Chicago, IL, 60607-7045, USA

Proceedings of the sixth annual conference on Computational learning theory - COLT '93, 1993

We consider generalizations of the PAC model, where the learning algorithms are also allowed to a... more We consider generalizations of the PAC model, where the learning algorithms are also allowed to ask different types of queries. There are several difficult problems that become efficiently learnable in these models, e.g. DFA are polynomially PAC learnable with membership queries (Angluin (1987)) and conjunctive concepts over structural domains with a bounded number of objects per scene are polynomially PAC learnable with restricted subset queries (Haussler (1989)). For PAC learning algorithms that may use random examples, any Boolean queries (i.e. queries with a yes/no answer) and equivalence queries, it is shown that the number of random examples and queries is fl(VC(C ) ), where VC(C) is the Vapnik-Chervonenkis dimension of the concept clsss C. This generalizes rsults of Blumer, Ehrenfeucht, Hauesler and Warmuth (1989) and Maase and Turzin (1989), and continues the work of Eisenberg and Rivest (1990) on lower bounds for generalized PAC models. The proof usea a combination of adversary and counting arguments.

Automata, Languages and Programming, 1991

... There are several lower bound results for this function in different models, using the fact t... more ... There are several lower bound results for this function in different models, using the fact that its table is an Haxiamard matrix (TarjŁn (1975), Chor and Goldreich (1985), Babai, Frankl and Simon (1986), Hajnai, Maass, Pudl~k, Szegedy and TurŁn (1987), Bruck (1990)). ...

Journal of Computer and System Sciences, 1987

We give a C" lower bound for read-once-only branching programs computing an explicit Boolean func... more We give a C" lower bound for read-once-only branching programs computing an explicit Boolean function. For n = (;), the function computes the parity of the number of triangles in a graph on v vertices. This improves previous exp(c &) lower bounds for other graph functions by Wegener and Zak. The result implies a linear lower bound for the space complexity of this Boolean function on "eraser machines," i.e., machines that erase each input bit immediately after having read it.

Information and Computation, 2022

Lower and upper bounds are given for the number of prototypes required for various nearest neighb... more Lower and upper bounds are given for the number of prototypes required for various nearest neighbor representations of Boolean functions.

Discrete Mathematics & Theoretical Computer Science, Aug 16, 2012

A formal framework is given for the characterizability of a class of belief revision operators, d... more A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a definability property of the class of partial orders in monadic second-order logic. Based on a non-definability result for a class of partial orders, an example is given of a non-characterizable class of revision operators. This appears to be the first non-characterizability result in belief revision.

We give a revision algorithm for monotone DNF formulas in the general revision model (additions a... more We give a revision algorithm for monotone DNF formulas in the general revision model (additions and deletions of variables) that uses O(m 3 e log n) queries, where m is the number of terms, e the revision distance to the target formula, and n the number of variables. We also give an algorithm for revising 2-term unate DNF formulas in the same model, with a similar query bound. Lastly, we show that the earlier query bound on revising readonce formulas in the deleti...

Fundamentals of Computation Theory, 1981

Proceedings of a Workshop on Computational Learning Theory and Natural Learning Systems Constraints and Prospects Constraints and Prospects, Aug 25, 1994

Lecture Notes in Computer Science, 1997

Lecture Notes in Computer Science, 1991

In the introduction of his paper starting computational learning theory, Valiant observed that th... more In the introduction of his paper starting computational learning theory, Valiant observed that the intuitive notion of learning merits similar attention from the point of view of formal theoretical study as that of the notion of computing. In this comparison, learning appears to be more elusive, more difficult to capture by a unified mathematical theory (as noted by Haussler (1990), it is not clear whether such a theory is even possible or desirable). Research was focused on concept learning, which is in fact closely related to computing in that several approaches developed in theoretical computer science can be adapted to its study. Interesting connections were found with other fields such as combinatorial optimization, cryptography and statistical pattern recognition. In this survey we gave a short account of some aspects of the results obtained in computational learning theory, by describing several learning models, characterizations of learnability, some learning algorithms and negative results.

Lecture Notes in Computer Science, 1991

... There are several lower bound results for this function in different models, using the fact t... more ... There are several lower bound results for this function in different models, using the fact that its table is an Haxiamard matrix (TarjŁn (1975), Chor and Goldreich (1985), Babai, Frankl and Simon (1986), Hajnai, Maass, Pudl~k, Szegedy and TurŁn (1987), Bruck (1990)). ...

Theoretical Advances in Neural Computation and Learning, 1994

Proceedings of the eleventh annual conference on Computational learning theory - COLT' 98, 1998

We consider the learnability of some concept classes in predicate logic with proper equivalence q... more We consider the learnability of some concept classes in predicate logic with proper equivalence queries. Concepts are represented by atomic formulas over a restricted language. The concept represented by an atomic formula consists of its ground instances having bounded depth. In addition, it is assumed that there is a first-order sentence given, and the COIIcept class contains only those atomic forrnulas which satisfy this sentence. For instance, one may consider the learnability of atomic formulas that represent symmetric, or transitive concepts. It is shown that every such concept class can be learned with O(m2 +m log n) queries, where m is the quantifier rank of the sentence and n is the depth bound for the ground instances. The proof uses a combination of tools from logic and learning algorithms for geometric concepts. Model theoretic games are used to determine the structure of the concept classes. We formulate a constrained version of the problem of learning two-dimensional axis-parallel rectangles, where one corner is required to belong to a prespecified subset. A sufficient condition is given for the efficient learnability of a rectangle in terms of the geometric properties of this subset. The algorithm for the predicate logic learning problem is obtained by combining the learning algorithm for the constrained rectangle learning problem with the informa*Current affiliation: Investment Technologies International, Chicago, IL. +Artificial Intelligence Research Croup of the Hungarian Academy of Sciences, Szeged, Hungary. Partially supported by grmts ESPRIT 20237 and OTKA T-016349 Permission to make digital or hard copies ofall or part ofthis work for personal or chxssroom use is granted without fee provided that copies are not made or distributed for prolit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to rrpuhlish, IO post on servers or to redistribute to lists, requires prior spccikic permission and/or a fee. COLT 98 Madison WI USA Copyright ACM 1998 I-581 13-057--O/98/ 7...$5.00 Gyiirgy Tur6n t Department of MSCS University of Illinois at Chicago 851 S.Morgan, M/C 249 Chicago, IL, 60607-7045, USA

Proceedings of the sixth annual conference on Computational learning theory - COLT '93, 1993

We consider generalizations of the PAC model, where the learning algorithms are also allowed to a... more We consider generalizations of the PAC model, where the learning algorithms are also allowed to ask different types of queries. There are several difficult problems that become efficiently learnable in these models, e.g. DFA are polynomially PAC learnable with membership queries (Angluin (1987)) and conjunctive concepts over structural domains with a bounded number of objects per scene are polynomially PAC learnable with restricted subset queries (Haussler (1989)). For PAC learning algorithms that may use random examples, any Boolean queries (i.e. queries with a yes/no answer) and equivalence queries, it is shown that the number of random examples and queries is fl(VC(C ) ), where VC(C) is the Vapnik-Chervonenkis dimension of the concept clsss C. This generalizes rsults of Blumer, Ehrenfeucht, Hauesler and Warmuth (1989) and Maase and Turzin (1989), and continues the work of Eisenberg and Rivest (1990) on lower bounds for generalized PAC models. The proof usea a combination of adversary and counting arguments.