REGULAR LANGUAGES: TO FINITE AUTOMATA AND BEYOND - SUCCINCT DESCRIPTIONS AND OPTIMAL SIMULATIONS

\uc8 noto che i linguaggi regolari \u2014 o di tipo 3 \u2014 sono equivalenti agli automi a stati finiti. Tuttavia, in letteratura sono presenti altre caratterizzazioni di questa classe di linguaggi, in termini di modelli riconoscitori e grammatiche. Per esempio, limitando le risorse computazionali di modelli pi\uf9 generali, quali grammatiche context-free, automi a pila e macchine di Turing, che caratterizzano classi di linguaggi pi\uf9 ampie, \ue8 possibile ottenere modelli che generano o riconoscono solamente i linguaggi regolari. I dispositivi risultanti forniscono delle rappresentazioni alternative dei linguaggi di tipo 3, che, in alcuni casi, risultano significativamente pi\uf9 compatte rispetto a quelle dei modelli che caratterizzano la stessa classe di linguaggi. Il presente lavoro ha l\u2019obiettivo di studiare questi modelli formali dal punto di vista della complessit\ue0 descrizionale, o, in altre parole, di analizzare le relazioni tra le loro dimensioni, ossia il numero di simboli utilizzati per specificare la loro descrizione. Sono presentati, inoltre, alcuni risultati connessi allo studio della famosa domanda tuttora aperta posta da Sakoda e Sipser nel 1978, inerente al costo, in termini di numero di stati, per l\u2019eliminazione del nondeterminismo dagli automi stati finiti sfruttando la capacit\ue0 degli automi two-way deterministici di muovere la testina avanti e indietro sul nastro di input.It is well known that regular \u2014 or type 3 \u2014 languages are equivalent to finite automata. Nevertheless, many other characterizations of this class of languages in terms of computational devices and generative models are present in the literature. For example, by suitably restricting more general models such as context-free grammars, pushdown automata, and Turing machines, that characterize wider classes of languages, it is possible to obtain formal models that generate or recognize regular languages only. The resulting formalisms provide alternative representations of type 3 languages that may be significantly more concise than other models that share the same expressing power. The goal of this work is to investigate these formal systems from a descriptional complexity perspective, or, in other words, to study the relationships between their sizes, namely the number of symbols used to write down their descriptions. We also present some results related to the investigation of the famous question posed by Sakoda and Sipser in 1978, concerning the size blowups from nondeterministic finite automata to two-way deterministic finite automata

Programming Using Automata and Transducers

Automata, the simplest model of computation, have proven to be an effective tool in reasoning about programs that operate over strings. Transducers augment automata to produce outputs and have been used to model string and tree transformations such as natural language translations. The success of these models is primarily due to their closure properties and decidable procedures, but good properties come at the price of limited expressiveness. Concretely, most models only support finite alphabets and can only represent small classes of languages and transformations. We focus on addressing these limitations and bridge the gap between the theory of automata and transducers and complex real-world applications: Can we extend automata and transducer models to operate over structured and infinite alphabets? Can we design languages that hide the complexity of these formalisms? Can we define executable models that can process the input efficiently? First, we introduce succinct models of transducers that can operate over large alphabets and design BEX, a language for analysing string coders. We use BEX to prove the correctness of UTF and BASE64 encoders and decoders. Next, we develop a theory of tree transducers over infinite alphabets and design FAST, a language for analysing tree-manipulating programs. We use FAST to detect vulnerabilities in HTML sanitizers, check whether augmented reality taggers conflict, and optimize and analyze functional programs that operate over lists and trees. Finally, we focus on laying the foundations of stream processing of hierarchical data such as XML files and program traces. We introduce two new efficient and executable models that can process the input in a left-to-right linear pass: symbolic visibly pushdown automata and streaming tree transducers. Symbolic visibly pushdown automata are closed under Boolean operations and can specify and efficiently monitor complex properties for hierarchical structures over infinite alphabets. Streaming tree transducers can express and efficiently process complex XML transformations while enjoying decidable procedures

New Results on Context-Free Tree Languages

Context-free tree languages play an important role in algebraic semantics and are applied in mathematical linguistics. In this thesis, we present some new results on context-free tree languages

Evaluation of XPath Queries against XML Streams

XML is nowadays the de facto standard for electronic data interchange on the Web. Available XML data ranges from small Web pages to ever-growing repositories of, e.g., biological and astronomical data, and even to rapidly changing and possibly unbounded streams, as used in Web data integration and publish-subscribe systems. Animated by the ubiquity of XML data, the basic task of XML querying is becoming of great theoretical and practical importance. The last years witnessed efforts as well from practitioners, as also from theoreticians towards defining an appropriate XML query language. At the core of this common effort has been identified a navigational approach for information localization in XML data, comprised in a practical and simple query language called XPath. This work brings together the two aforementioned ``worlds'', i.e., the XPath query evaluation and the XML data streams, and shows as well theoretical as also practical relevance of this fusion. Its relevance can not be subsumed by traditional database management systems, because the latter are not designed for rapid and continuous loading of individual data items, and do not directly support the continuous queries that are typical for stream applications. The first central contribution of this work consists in the definition and the theoretical investigation of three term rewriting systems to rewrite queries with reverse predicates, like parent or ancestor, into equivalent forward queries, i.e., queries without reverse predicates. Our rewriting approach is vital to the evaluation of queries with reverse predicates against unbounded XML streams, because neither the storage of past fragments of the stream, nor several stream traversals, as required by the evaluation of reverse predicates, are affordable. Beyond their declared main purpose of providing equivalences between queries with reverse predicates and forward queries, the applications of our rewriting systems shed light on other query language properties, like the expressivity of some of its fragments, the query minimization, or even the complexity of query evaluation. For example, using these systems, one can rewrite any graph query into an equivalent forward forest query. The second main contribution consists in a streamed and progressive evaluation strategy of forward queries against XML streams. The evaluation is specified using compositions of so-called stream processing functions, and is implemented using networks of deterministic pushdown transducers. The complexity of this evaluation strategy is polynomial in both the query and the data sizes for forward forest queries and even for a large fragment of graph queries. The third central contribution consists in two real monitoring applications that use directly the results of this work: the monitoring of processes running on UNIX computers, and a system for providing graphically real-time traffic and travel information, as broadcasted within ubiquitous radio signals

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science