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Easton functions and supercompactness

Brent Cody, Sy-David Friedman, Radek Honzik (2014)

Fundamenta Mathematicae

Suppose that κ is λ-supercompact witnessed by an elementary embedding j: V → M with critical point κ, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton’s theorem: (1) ∀α α < cf(F(α)), and (2) α < β ⇒ F(α) ≤ F(β). We address the question: assuming GCH, what additional assumptions are necessary on j and F if one wants to be able to force the continuum function to agree with F globally, while preserving...

Easy lambda-terms are not always simple

Alberto Carraro, Antonino Salibra (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A closed λ-term M is easy if, for any other closed term N, the lambda theory generated by M = N is consistent. Recently, it has been introduced a general technique to prove the easiness of λ-terms through the semantical notion of simple easiness. Simple easiness implies easiness and allows to prove consistency results via construction of suitable filter models of λ-calculus living in the category of complete partial orderings: given a simple easy term M and an arbitrary closed term N, it is possible...

Easy lambda-terms are not always simple

Alberto Carraro, Antonino Salibra (2012)

RAIRO - Theoretical Informatics and Applications

A closed λ-term M is easy if, for any other closed term N, the lambda theory generated by M = N is consistent. Recently, it has been introduced a general technique to prove the easiness of λ-terms through the semantical notion of simple easiness. Simple easiness implies easiness and allows to prove consistency results via construction of suitable filter models of λ-calculus living in the category of complete partial orderings: given ...

Effect algebras and ring-like structures

Enrico G. Beltrametti, Maciej J. Maczyński (2003)

Discussiones Mathematicae - General Algebra and Applications

The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring multiplication non-distributive with respect to addition. By some natural assumption on the effect algebra,...

Effective decomposition of σ-continuous Borel functions

Gabriel Debs (2014)

Fundamenta Mathematicae

We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering ( A ) n ω of X such that f | A is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

Efficient simulation of synchronous systems by multi-speed systems

Tomasz Jurdziński, Mirosław Kutyłowski, Jan Zatopiański (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the number...

Efficient simulation of synchronous systems by multi-speed systems

Tomasz Jurdziński, Mirosław Kutyłowski, Jan Zatopiański (2010)

RAIRO - Theoretical Informatics and Applications

We consider systems consisting of finite automata communicating by exchanging messages and working on the same read-only data. We investigate the situation in which the automata work with constant but different speeds. We assume furthermore that the automata are not aware of the speeds and they cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata. Complexity measure that we consider here is the...

Efficient weighted expressions conversion

Faissal Ouardi, Djelloul Ziadi (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε -free nondeterministic finite automaton having O ( n ) states and O ( n log 2 ( n ) ) transitions. This method has been implemented efficiently in O ( n log 2 ( n ) ) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O ( n log 2 ( n ) ) time.

Efficient weighted expressions conversion

Faissal Ouardi, Djelloul Ziadi (2007)

RAIRO - Theoretical Informatics and Applications

J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε-free nondeterministic finite automaton having O(n) states and O(nlog2(n)) transitions. This method has been implemented efficiently in O(nlog2(n)) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O(nlog2(n)) time.

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