A Parry number is a real number β > 1 such that the Rényi β-expansion of 1 is finite or infinite eventually periodic. If this expansion is finite, β is said to be a simple Parry number. Remind that any Pisot number is a Parry number. In a previous work we have determined the complexity of the fixed point uβ of the canonical substitution associated with β-expansions, when β is a simple Parry num...

We consider the problem of when a symbolic dynamical system supports Borel probability measure that is invariant under every element its automorphism group. It follows readily from classical result Parry full shift on finitely many symbols, and more generally any mixing subshift finite type, such measure. Frisch Tamuz recently dubbed measures characteristic, further showed zero entropy has char...

Parry discusses an extension of Aristotle’s syllogistic that uses four nontraditional quantifiers. We show that his conjectured decision procedure for validity for the extended syllogistic is correct even if syllogisms have more than two premises. And we axiomatize this extension of the syllogistic. 1 Background and motivation Parry [2] discusses an extension of the syllogistic in which sentenc...

Several ways of assigning probabilities to runs of timed automata (TA) have been proposed recently. When only the TA is given, a relevant question is to design a probability distribution which represents in the best possible way the runs of the TA. This question does not seem to have been studied yet. We give an answer to it using a maximal entropy approach. We introduce our variant of stochast...

Several ways of assigning probabilities to runs of timed automata (TA) have been proposed recently. When only the TA is given, a relevant question is to design a probability distribution which represents in the best possible way the runs of the TA. This question does not seem to have been studied yet. We give an answer to it using a maximal entropy approach. We introduce our variant of stochast...