This thesis investigates multi pushdown automata and introduces their   new modifications based on deep pushdown.  The first modification is Input driven multi deep pushdown automata, which has several deep pushdown lists and the current input symbol determines whether the automaton performs a push operation, a pop operation, an expansion operation or does not touch the stack. The second introduced modification is Regulated pushdown automata by deep pushdown. In addition to ordinary pushdowns, this version contains deep pushdown, which is used to generate the control language. This thesis proves, that the acceptance power of the described variants  is equal to the accepting power of Turing machines.  This thesis also contains view on program realisation of theoretical models, which were described in the theoretical part and introduces a library for the syntax analysis, which is based on it.

Pushdown systems equip a finite state system with an unbounded stack memory, and are thus infinite state. By recording the call history on the stack, these systems provide a natural model for recursive procedure calls. Model-checking for pushdown systems has been well-studied. Tools implementing pushdown model-checking (e.g. Moped) are an essential back-end component of high-profile software model checkers such as SLAM, Blast and Terminator. Higher-order pushdown systems define a more complex memory structure: a higher-order stack is a stack of lower-order stacks. These systems form a robust hierarchy closely related to the Caucal hierarchy and higher-order recursion schemes. This latter connection demonstrates their importance as models for programs with higher-order functions. We study the global model-checking problem for (higher-order) pushdown systems. In particular, we present a new algorithm for computing the winning regions of a parity game played over an order-1 pushdown system. We then show how to compute the winning regions of two-player reachability games over order-n pushdown systems. These algorithms extend the saturation methods of Bouajjani, Esparza and Maler for order-1 pushdown systems, and Bouajjani and Meyer for higher-order pushdown systems with a single control state. These techniques begin with an automaton recognising (higher-order) stacks, and iteratively add new transitions until the automaton becomes saturated. The reachability result, presented at FoSSaCS 2007 and in the LMCS journal, is the main contribution of the thesis. We break the saturation paradigm by adding new states to the automaton during the iteration. We identify the fixed points required for termination by tracking the updates that are applied, rather than by observing the transition structure. We give a number of applications of this result to LTL model-checking, branching-time model-checking, non-emptiness of higher-order pushdown automata and Büchi games. Our second major contribution is the first application of the saturation technique to parity games. We begin with a mu-calculus characterisation of the winning region. This formula alternates greatest and least fixed point operators over a kind of reachability formula. Hence, we can use a version of our reachability algorithm, and modifications of the Büchi techniques, to compute the required result. The main advantages of this approach compared to existing techniques due to Cachat, Serre and Vardi et al. are that it is direct and that it is not immediately exponential in the number of control states, although the worst-case complexity remains the same.

This paper addresses the issue of design and implementation of syntactic analysis based on the context sensitive languages, respectively, grammars that contains constructs, which isn't possible to analyze with the help of the standard parsers based on the context free grammars. More specifically, this paper deals with the possibility of adding context sensitive support to the classic LL-analysis by replacing the standard pushdown automata (PDA) with deep pushdown automata (DP), which were introduced and published by prof. Alexander Meduna.

This thesis defines and studies two new types of automata, cooperating distributed pushdown automata systems (CDPDAS) and parallel communicating pushdown automata systems (PCPDAS).  CDPDAS and PCPDAS adapt the main concept of cooperating distributed grammar systems (CDGS) and parallel communicating automata systems (PCPDAS), respectively.  CDPDAS are proven to have the same power as PDA and this thesis further explores the reason why CDPDAS do not increase power while CDGS do and introduces an automata system inspired by CDPDAS that does increase the power.  PCGS have similar power as CDGS, but PCPDAS are equvalent with TM, which is proven by creating a communication protocol to access a second stack.

Higher-Order Pushdown Automata (HOPDA) are abstract machines equipped with a nested stacks of stacks ... of stacks of stacks. Collapsible pushdown automata (CPDA) enhance these stacks with the addition of ‘links’ emanating from atomic elements to the higher-order stacks below. For trees CPDA are equi-expressive with recursion schemes, which can be viewed as simply-typed λY terms. With vanilla HOPDA, one can only capture schemes satisfying a syntactic constraint called safety. This dissertation begins with some results concerning the significance of links in terms of recursion schemes. We introduce a fine-grained notion of safety that allows us to correlate the need for links of a given order with the imposition of safety on variables of a corresponding order. This generalises some joint work with William Blum that shows we can dispense with homogeneous types when characterising safety. We complement this result with a demonstration that homogeneity by itself does not constrain the expressivity of otherwise unrestricted recursion schemes. The main results of the dissertation, however, concern the configuration graphs of CPDA. Whilst the configuration graphs of HOPDA are well understood and have decidable MSO theories (they coincide with the Caucal hierarchy), relatively little is known about the transition graphs of CPDA. It is known that they already have undecidable MSO theories at order-2, but Kartzow recently showed that 2-CPDA graphs are tree automatic and hence first-order logic is decidable at order-2. We provide a characterisation of the decidability of first-order logic on CPDA graphs in terms of quantifier-alternation and the order of CPDA stacks and the links contained within. Whilst this characterisation is fairly comprehensive, we do leave open the question of decidability for some sub-classes of CPDA. It turns out that decidability can be highly sensitive to the order of links in a stack relative to the order of the stack itself. In addition to some strong and surprising undecidability results, we also develop further Kartzow’s work on 2-CPDA. We introduce prefix-rewrite systems for nested-words that characterise the configuration graphs of both 2-CPDA and 2-HOPDA, capturing the power of collapse precisely in terms outside of the language of CPDA. It also formalises and demonstrates the inherent asymmetry of the collapse operation. This generalises the rational prefix-rewriting systems characterising conventional pushdown graphs and we believe establishes the 2-CPDA graphs as an interesting and robust class.

Pro přirozené číslo n, n-expandovatelné hluboké zasobníkové automaty vždy obsahují maximálně n výskytů nevstupních symbolů v jejich zásobníku v průběhu jakékoli kompilace. Jako hlavní výsledek, tato práce demonstruje, že tyto automaty mají stejnou vyjadřovací sílu jako automaty s #, nacházející pouze na dně zásobníku, a jediným dalším nevstupním symbolem. Z tohoto závěru vyplývá nekonečná hierarchie jazyků přijímaných těmito automaty.

This thesis is a continuation of my bachelor thesis, which is dedicated to syntax analysis based on deep pushdown automata. In theorical part of this thesis is defined everything fundamental for this work, for example deep syntax-directed translation, pushdown automata, deep pushdown automata, finite transducer and deep pushdown transducer.   The second part of this thesis is dedicated to the educational program for students of IFJ. In this part is defined strucure of this program and its parts. All part of program are analyzed from a theoretical and practical point of view.

Büchi, Elgot and Trakhtenbrot provided a seminal connection between monadic second-order logic and finite automata for both finite and infinite words. This BET- Theorem has been extended by Lautemann, Schwentick and Thérien to context-free languages by introducing a monadic second-order logic with an additional existentially quantified second-order variable. This new variable models the stack of pushdown au- tomata. A fundamental study by Cohen and Gold extended the context-free languages to infinite words. Our first main result is a second-order logic in the sense of Lautemann, Schwentick and Thérien with the same expressive power as ω-context-free languages. For our argument, we investigate Greibach normal forms of ω-context-free grammars as well as a new type of Büchi pushdown automata, the simple pushdown automata. Simple pushdown automata do not use e-transitions and can change the stack only by at most one symbol. We show that simple pushdown automata of infinite words suffice to accept all ω-context-free languages. This enables us to use Büchi-type results recently developed for infinite nested words. In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Weighted context-free languages of finite words trace back already to Chomsky and Schützenberger. Their work has been extended to infinite words by Ésik and Kuich. As in the theory of formal grammars, these weighted ω-context-free languages, or ω-algebraic series, can be represented as solutions of mixed ω-algebraic systems of equations and by weighted ω-pushdown automata. In our second main result, we show that (mixed) ω-algebraic systems can be trans- formed into Greibach normal form. We then investigate simple pushdown automata in the weighted setting. Here, we give our third main result. We prove that weighted simple pushdown automata of finite words recognize all weighted context-free languages, i.e., generate all algebraic series. Then, we show that weighted simple ω-pushdown automata generate all ω-algebraic series. This latter result uses the former result together with the Greibach normal form that we developed for ω-algebraic systems. As a fourth main result, we prove that for weighted simple ω-pushdown automata, Büchi-acceptance and Muller-acceptance are expressively equivalent. In our fifth main result, we derive a Nivat-like theorem for weighted simple ω- pushdown automata. This theorem states that the behaviors of our automata are precisely the projections of very simple ω-series restricted to ω-context-free languages. The last result, our sixth main result, is a weighted logic with the same expressive power as weighted simple ω-pushdown automata. To prove the equivalence, we use a similar result for weighted nested ω-word automata and apply our present result of expressive equivalence of Muller and Büchi acceptance.

Graph-structured data (GSD) is a popular model to represent complex information in a wide variety of applications such as social networks, biological data management, digital libraries, and traffic networks. The flexibility of this model allows the information to evolve and easily integrate with heterogeneous data from many sources. In this dissertation we study three important problems on GSD. A consistent theme of our work is the use of automata methods and techniques to process and reason about GSD. First, we address the problem of answering queries on GSD in a distributed environment. We focus on regular path queries (RPQs) – given by regular expressions matching paths in graph-data. RPQs are the building blocks of almost any mechanism for querying GSD. We present a fault-tolerant, message-efficient, and truly distributed algorithm for answering RPQs. Our algorithm works for the larger class of weighted RPQs on weighted GSDs. Second, we consider the problem of answering RPQs on incomplete GSD, where different data sources are represented by materialized database views. We explore the connection between “certain answers” (CAs) and answers obtained from “view-based rewritings” (VBRs) for RPQs. CAs are answers that can be obtained on each database consistent with the views. Computing all of CAs for RPQs is NP-hard, and one has to resort to an exponential algorithm in the size of the data–view materializations. On the other hand, VBRs are query reformulations in terms of the view definitions. They can be used to obtain query answers in polynomial time in the size of the data. These answers are CAs, but unfortunately for RPQs, not all of the CAs can be obtained in this way. In this work, we show the surprising result that for RPQs under local semantics, using VBRs to answer RPQs gives all the CAs. The importance of this result is that under such semantics, the CAs can be obtained in polynomial time in the size of the data. Third, we focus on XML–an important special case of GSD. The scenario we consider is streaming XML between exchanging parties. The problem we study is flexible validation of streaming XML under the realistic assumption that the schemas of the exchanging parties evolve, and thus diverge from one another. We represent schemas by using Visibly Pushdown Automata (VPAs), which recognize Visibly Pushdown Languages (VPLs). We model evolution for XML by defining formal language operators on VPLs. We show that VPLs are closed under the defined language operators and this enables us to expand the schemas (for XML) in order to account for flexible or constrained evolution. / Graduate

The present work proposes visibly pushdown transducers (VPTs) for defining transformations of documents with a nesting structure. We show that this subclass of pushdown transducers enjoy good properties. Notably, we show that functionality is decidable in PTime and k-valuedness in co-NPTime. While this class is not closed under composition and its type checking problem against visibly pushdown automata is undecidable, we identify a subclass, the well-nested VPTs, closed under composition and with a decidable type checking problem. Furthermore, we show that the class of VPTs is closed under look-ahead, and that the deterministic VPTs with look-ahead characterize the functional VPTs transductions. Finally, we investigate the resources necessary to perform transformations defined by VPTs. We devise a memory efficient algorithm. Then we show that it is decidable whether a VPT transduction can be performed with a memory that depends on the level of nesting of the input document but not on its length. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished