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Algebraiccoalgebraic specification in CoCasl
 J. LOGIC ALGEBRAIC PROGRAMMING
, 2006
"... We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the wellknown coalgebraic modal logic can be expressed in CoCasl. We present sufficient criter ..."
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We introduce CoCasl as a simple coalgebraic extension of the algebraic specification language Casl. CoCasl allows the nested combination of algebraic datatypes and coalgebraic process types. We show that the wellknown coalgebraic modal logic can be expressed in CoCasl. We present sufficient criteria for the existence of cofree models, also for several variants of nested cofree and free specifications. Moreover, we describe an extension of the existing proof support for Casl (in the shape of an encoding into higherorder logic) to CoCasl.
That SnS Can Be Modally Characterized
, 1996
"... We show that a modal mucalculus with label set f1; : : : ; ng can define the Rabin recognizable tree languages up to an equivalence similar to the observational equivalence of Milner. 1 Introduction In [11] it was shown that the temporal logic ETL [10] can define exactly the class of !regular lan ..."
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We show that a modal mucalculus with label set f1; : : : ; ng can define the Rabin recognizable tree languages up to an equivalence similar to the observational equivalence of Milner. 1 Introduction In [11] it was shown that the temporal logic ETL [10] can define exactly the class of !regular languages. In [7] it was shown that a fixedpoint calculus whose signature apart from maximal and minimal fixed points and disjunction includes the usual operators on trees can define exactly the sets of infinite trees recognized by Rabin tree automata [8]; this class of sets corresponds to the class of structures definable in the secondorder monadic theory of n successors, SnS . It would be nice if one could show that a branching time temporal logic has the same expressive power as SnS ; after all, branching time temporal logics are interpreted on computation trees. In [4] it is shown that a restricted version of SnS with set quantification restricted to paths is expressively equivalent to C...
www.elsevier.com/locate/tcs Ambiguous classes in calculi hierarchies
"... A classical result by Rabin states that if a set of trees and its complement are both Büchi definable in the monadic second order logic, then these sets are weakly definable. In the language of calculi, this theorem asserts the equality between the complexity classes 2 ∩2 and Comp(1,1) of the fixed ..."
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A classical result by Rabin states that if a set of trees and its complement are both Büchi definable in the monadic second order logic, then these sets are weakly definable. In the language of calculi, this theorem asserts the equality between the complexity classes 2 ∩2 and Comp(1,1) of the fixedpoint alternationdepth hierarchy of the calculus of tree languages. It is natural to ask whether at higher levels of the hierarchy the ambiguous classes n+1 ∩n+1 and the composition classes Comp(n,n) are equal, and for which calculi. The first result of this paper is that the alternationdepth hierarchy of the games calculus—whose canonical interpretation is the class of all complete lattices—enjoys this property. More explicitly, every parity gamewhich is equivalent both to a game inn+1 and to a game inn+1 is also equivalent to a game obtained by composing games in n andn. The second result is that the alternationdepth hierarchy of the calculus of tree languages does not enjoy the property. Taking into account that any Büchi definable set is recognized by a nondeterministic Büchi automaton, we generalize Rabin’s result in terms of the following separation theorem: if two disjoint languages are recognized by nondeterministicn+1 automata, then there exists a third