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15
Analytic Countably Splitting Families
 Journal of Symbolic Logic
, 1980
"... A family A P(!) is called countably splitting if for every countable F [!] , some element of A splits every member of F . We de ne a notion of a splitting tree, by means of which we prove that every analytic countably splitting family contains a closed countably splitting family. An applic ..."
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A family A P(!) is called countably splitting if for every countable F [!] , some element of A splits every member of F . We de ne a notion of a splitting tree, by means of which we prove that every analytic countably splitting family contains a closed countably splitting family. An application of this notion solves a problem of Blass.
Methods for the transformation of ωautomata: Complexity and connection to secondorder logic
, 1998
"... ..."
The extent of constructive game labellings
 Proceedings of the 5th Panhellenic Logic Symposium
, 2005
"... Abstract. We develop a theory of labellings for infinite trees, define the notion of a combinatorial labelling, and show that ∆ 0 2 is the largest boldface pointclass in which every set admits a combinatorial labelling. 1 ..."
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Abstract. We develop a theory of labellings for infinite trees, define the notion of a combinatorial labelling, and show that ∆ 0 2 is the largest boldface pointclass in which every set admits a combinatorial labelling. 1
Modal and Temporal Operators on Partial Orders
 Proc. 3rd Domain Workshop
, 1997
"... We generalize the operators of classical linear time temporal logic to partial orders, such as the ones used in domain theory. This relates denotaional semantics and temporal logic. We put this into the general perspective of modal logic. 2 and 3 are viewed as standard modalities, which gives "half ..."
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We generalize the operators of classical linear time temporal logic to partial orders, such as the ones used in domain theory. This relates denotaional semantics and temporal logic. We put this into the general perspective of modal logic. 2 and 3 are viewed as standard modalities, which gives "half " of the standard axioms of LTL. Moroever, we show that the nexttime operator fl can be defined as a combination of two modalities. We show the role of the standard LTL axioms in narrowing the underlying partial orders to linear ones generated by the immediatesuccessor relation. We distinguish between modal and temporal validity of formulas and investigate their relation. 1 Introduction In [11] a stream has been identified with the set of its finite prefixes. Based on this, we have used a special way of characterising sets of streams through sets of relevant finite "snapshots". Given a set P ` A where A is a set of atomic actions, states or data, we define str P def = f( v Q) : Q ` ...
A MultiAgent GraphGame Approach to Theoretical Foundations of Linguistic Geometry
 Proc. of the Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI 95
, 1995
"... The Linguistic Geometry (LG) approach to discrete systems was introduced by B. Stilman in early 80s. It employed competing/cooperating agents for modeling and controlling of discrete systems. The approach was applied to a variety of problems with huge state spaces including control of aircraft, batt ..."
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The Linguistic Geometry (LG) approach to discrete systems was introduced by B. Stilman in early 80s. It employed competing/cooperating agents for modeling and controlling of discrete systems. The approach was applied to a variety of problems with huge state spaces including control of aircraft, battlefield robots, and chess. One of the key innovations of LG is the use of almost winning strategies, rather than truly winning strategies for the participating agents. There are many cases where the winning strategies have so high time complexity that they are not computable in practice, whereas the almost winning strategies can be applied and they beat the opposing agent almost guaranteed. Independently of LG the idea of competing/ cooperating agents was employed in the late 80s by A. Nerode, A. Yakhnis, and V. Yakhnis (NYY) within their approach to modeling concurrent systems and, more recently, within the “Strategy Approach to Hybrid Systems ” developed for continuous systems by A. Nerode, W. Kohn, A. Yakhnis, and others.
Ideal stream algebra
 Lecture Notes in Computer Science 1546
, 1998
"... We provide some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is wellknown that the associated ideal completion provides a simple way of constructing algebraic cpos. An ideal can be viewed as a ..."
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We provide some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is wellknown that the associated ideal completion provides a simple way of constructing algebraic cpos. An ideal can be viewed as a set of consistent finite or compact approximations of an object which itself may even be infinite. A special case is the domain of streams where the finite approximations are the finite prefixes of a stream. We introduce a special way of characterising behaviours through sets of relevant approximations. This is a generalisation of the technique used earlier for the case of streams. Given a set P ` M of a partial order (M;), we define ide P: = fQ: Q ` P directedg; where Q
 Regular Languages Defined By A Limit Operator
, 1996
"... : Finite deterministic 1acceptor accepting both finite and infinite words over a finite alphabet is introduced. It is shown that 1regular languages can be defined as sets of 1words accepted by an 1acceptor. A limit operator on regular languages is used to define a special class of 1regular lan ..."
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: Finite deterministic 1acceptor accepting both finite and infinite words over a finite alphabet is introduced. It is shown that 1regular languages can be defined as sets of 1words accepted by an 1acceptor. A limit operator on regular languages is used to define a special class of 1regular languages. In 1acceptors accepting these languages incidence relations between the sets used for acceptance are determined. 1. Introduction The paper deals with special classes of 1regular languages. If a finite alphabet \Sigma is given, then by an 1regular language over \Sigma we understand the union of a regular and an !regular language over \Sigma. In this paper we show that it is possible to define such languages by means of a single finitestate device. A deterministic machine capable of constructing both finite and infinite sequences is first introduced in [7]. In [4] the structure of the sets constructed in [7] is investigated and in [5] a nondeterministic version of such machines ...
Refining Ideal Behaviours
, 1995
"... This paper provides some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is wellknown that the associated ideal completion [8] provides a simple way of constructing algebraic cpos. An ideal can be v ..."
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This paper provides some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is wellknown that the associated ideal completion [8] provides a simple way of constructing algebraic cpos. An ideal can be viewed as a set of consistent finite or compact approximations of an object which itself may even be infinite.