Using automata to characterise fixed point temporal logics

This work examines propositional fixed point temporal and modal logics called mu-calculi and their relationship to automata on infinite strings and trees. We use correspondences between formulae and automata to explore definability in mu-calculi and their fragments, to provide normal forms for formulae, and to prove completeness of axiomatisations. The study of such methods for describing infinitary languages is of fundamental importance to the areas of computer science dealing with non-terminating computations, in particular to the specification and verification of concurrent and reactive systems. To emphasise the close relationship between formulae of mu-calculi and alternating automata, we introduce a new first recurrence acceptance condition for automata, checking intuitively whether the first infinitely often occurring state in a run is accepting. Alternating first recurrence automata can be identified with mu-calculus formulae, and ordinary, non-alternating first recurrence automata with formulae in a particular normal form, the strongly aconjunctive form. Automata with more traditional Büchi and Rabin acceptance conditions can be easily unwound to first recurrence automata, i.e. to mu-calculus formulae. In the other direction, we describe a powerset operation for automata that corresponds to fixpoints, allowing us to translate formulae inductively to ordinary Büchi and Rabin-automata. These translations give easy proofs of the facts that Rabin-automata, the full mu-calculus, its strongly aconjunctive fragment and the monadic second-order calculus of n successors SnS are all equiexpressive, that Büchi-automata, the fixpoint alternation class Pi_2 and the strongly aconjunctive fragment of Pi_2 are similarly related, and that the weak SnS and the fixpoint-alternation-free fragment of mu-calculus also coincide. As corollaries we obtain Rabin's complementation lemma and the powerful decidability result of SnS. We then describe a direct tableau decision method for modal and linear-time mu-calculi, based on the notion of definition trees. The tableaux can be interpreted as first recurrence automata, so the construction can also be viewed as a transformation to the strongly aconjunctive normal form. Finally, we present solutions to two open axiomatisation problems, for the linear-time mu-calculus and its extension with path quantifiers. Both completeness proofs are based on transforming formulae to normal forms inspired by automata. In extending the completeness result of the linear-time mu-calculus to the version with path quantifiers, the essential problem is capturing the limit closure property of paths in an axiomatisation. To this purpose, we introduce a new \exists\nu-induction inference rule

Riddles: Perspectives on the use, function and change in a folklore genre

Riddles are a journey into a fascinating world rich in delightful metaphors and ambiguity. This book is based on material drawn from all over the world and analyses both traditional true riddles and contemporary joking questions. It introduces the reader to different riddling situations and the many functions of riddles, wich vary from education to teasing, and from defusing a heated situation to entertainment. In addition to providing a survey of international riddle scholarship, the book has a comprehensive bibliography with suggestions for further reading

Experience and Interpretation: Emotion as Revealed in Narration

I discuss in this article some key narratives of women I interviewed in Ingria 1992–1993. The narratives of those women were about dramatic stages of their lives during the World War II. The main themes of the life stories were forced transfers and deportation suffered by the Ingrian Finns. I examine with some examples how various paralinguistic devices, such as speech tempo, emotional outbursts or silence, were tied in with the verbalisation of experiences. The three factors I discuss here are woven into the narratives of the women I interviewed. The first factor is “impassioned narrating”, which shows how a narrator reveals how she is reliving the event, she told about. The second factor is weeping and we may ask how the tears affect the narrator. The third factor is silence and reticence. In retrospect I have thought about the therapeutic effect of speaking, forgetting and remaining silent

Pulsed standing-wave mirror for neutral atoms and molecules

Reflection of neutral atoms and molecules by a pulsed standing wave with a duration on the order of nanoseconds is studied. It is shown that, with a suitable choice of the laser parameter values, each period of the standing-wave pattern functions as an independent mirror, thus providing a novel way to manipulate large samples of neutral gas-phase particles even with a single laser pulse. At moderate field intensities, the pulsed standing-wave mirror would be directly applicable, e.g., for the manipulation of buffer-gas cooled molecules. Peer reviewe

Response to the letter by de Boer et al. (2022)

Non peer reviewe

Opiskelijapalaute : Opintoasiaintoimikunnan palautejaoksen loppuraportti

Peer reviewe