On distributive fixed-point expressions
On Distributive Fixed-Point Expressions
For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e' of alternation-depth 2 and size . Expression e' is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of the resulting expression.
On global induction mechanisms in a -calculus with explicit approximations
We investigate a Gentzen-style proof system for the first-order -calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantic...
On global induction mechanisms in a μ-calculus with explicit approximations
We investigate a Gentzen-style proof system for the first-order μ-calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantic...
On Lamport's comparison between linear and branching time temporal logic
On proofs of correctness of well-structured programs
On proofs of correctness of well-structured programs. II
On some arithmetically expressible properties of programs
On temporal program verification rules
On the Decidability of the Equivalence Problem for Monadic Recursive Programs
We present a uniform and easy-to-use technique for deciding the equivalence problem for deterministic monadic linear recursive programs. The key idea is to reduce this problem to the well-known group-theoretic problems by revealing an algebraic nature of program computations. We show that the equivalence problem for monadic linear recursive programs over finite and fixed alphabets of basic functions and logical conditions is decidable in polynomial time for the semantics based on the free monoids...
On the use of homomorphisms for proving the equivalence of some programs
Parallélisation sémantique
Permissive strategies : from parity games to safety games
It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding...
Permissive strategies: from parity games to safety games
It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...
Probabilistic evaluation of fuzzy quantified sentences: independence profile.
This paper describes a classification for fuzzy quantifiers that makes it possible to include a significant number of cases of interest (exception, comparatives). All quantifiers therein described can be evaluated by following a fuzzy model with probabilistic interpretation, based on the Theory of Generalized Quantifiers.
Program flow analysis for reducing and estimating the cost of test coverage criteria. (Abstract).
Proposal for a natural formalization of functional programming concepts
Refinements of inductive inference by Popperian and reliable machines
Regular languages definable by Lindström quantifiers
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.
Regular languages definable by Lindström quantifiers
In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.