Generalizing input-driven languages: Theoretical and practical benefits

Abstract

Abstract. Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families.

Operator precedence temporal logic and model checking

“…In order to see how the syntactic structure of a sentence is determined by the OPM and is formalized by the concept of chain, let us apply the traditional operator precedence parsing algorithm to the sample word w ex = call han call call thr thr ret (for a more complete treatment, cf. [29,32]). First, write all precedence relations between consecutive characters, according to OPM M call .…”

“…The distinguishing feature of OPLs, in fact, is that during their parsing nonterminals are "transparent". This justifies labeling them as input-driven but not visible push-down languages ( [29]). Notice how each chain body corresponds to the expansion of one non-terminal (represented by a dot in the figure).…”

“…All in all OPLs appear to enjoy many if not all of the pleasant algebraic and logic properties of structured CFLs but widen their application field in a dramatic way. For a more comprehensive description of OPL properties and their relations with other CFL subfamilies see [29].…”

Temporal Logic and Model Checking for Operator Precedence Languages

“…All above definitions are extended to the case of infinite strings in the traditional way [17]; for this reason and for the sake of brevity we will deal with the ω-case only in Section 5.1 where the application of novel techniques is necessary. For a more complete description of the OPL family and of its relations with other CFLs we refer the reader to [18].…”

“…NWTL is a temporal logic based on the VPL family, which is strictly contained in OPL. In [10,17,18] the relations between the two families are discussed in depth both from a mathematical and an application point of view: building OPTL formulas describing OPLs that are not VPLs is a trivial job. This proves that there exist languages not expressible in NWTL that can be expressed in OPTL.…”