Floyd Languages for Infinite Words Linguaggi Di Floyd per Parole Infinite

Nowadays many software systems are designed to work without interruption: for instance operating systems are required to provide continuously their services to the users, and web applications and verification of critical and concurrent systems represent a typical scenario where endless computations are involved. The behavior of systems operating forever can be formally specified by means of ω-languages, a class of languages defined as sets of infinite words of symbols. Theory on ω-languages dates back to the sixties, with the pioneering works of Büchi and Muller on finite-state automata able to recognize infinite strings( [5], [19]). More recently, ω-languages have been studied in [2] as an extension of Visibly Pushdown Languages (VPL), a class of deterministic context-free languages which model strings as nested words of symbols. This work of thesis follows this line of research with the aim of investigating Floyd languages (FL), a traditional formalism introduced in [12] and rediscovered in the recent work [8], generalizing them to languages of infinite words. FLs are one of the early classes of Deterministic Context-Free (DCF) languages and are defined by operator precedence grammars, renamed Floyd Grammars (FG) in [8]. Research on FLs began decades ago (from the first work of Floyd, [12], and [9]) and has been then interrupted after the introduction of advanced parsing techniques for more expressive languages, as LR(k). Renewal of interest in the study of FLs, which motivates the investigation carried on in this thesis, derived from the discovery of recent surprising results: along the path of research on parentheses-like languages resumed with the definition of VPLs and their characterization in terms of a class of automata (named Visibly Pushdown Automata), recent studies revealed the potential of FLs, proving that FLs are a proper superclass of VPLs and represent the largest known DCF family closed under all classical operations enjoyed by regular languages. Furthermore, the recent paper [17] characterized FLs by means of a complementary class of stack-based automata (Floyd Automata) and this result leads quite naturally to a further interesting extension of FLs to ω-languages. The main issue of this thesis is, thus, the investigation of this novel class of ω-languages and the focus of this study consists in the characterization of suitable abstract machines to define these languages. More to the point, ω-languages have been traditionally characterized in terms of finite-state automata, augmented with different kinds of properties and acceptance conditions which completely determine their expressive power. Classical conditions on how ω-automata recognize strings refer to the sequence of states of the automata occurring in the computation for the acceptance of a word: typical requirements, named after their authors, as Büchi, Muller and Rabin [21] conditions, constrain in particular ways the set of states belonging to these sequences and that are visited infinitely often. The distinguishing feature of FLs w.r.t. classical regular ω-languages is that they define context-free languages and their corresponding automata are endowed with a non-finite memory unit.