On Functionality of Visibly Pushdown Transducers

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.Comment: 20 page

Streamability of nested word transductions

We consider the problem of evaluating in streaming (i.e., in a single left-to-right pass) a nested word transduction with a limited amount of memory. A transduction T is said to be height bounded memory (HBM) if it can be evaluated with a memory that depends only on the size of T and on the height of the input word. We show that it is decidable in coNPTime for a nested word transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In this case, the required amount of memory may depend exponentially on the height of the word. We exhibit a sufficient, decidable condition for a VPT to be evaluated with a memory that depends quadratically on the height of the word. This condition defines a class of transductions that strictly contains all determinizable VPTs

Transducer-Based Rewriting Games for Active XML

Context-free games are two-player rewriting games that are played on nested strings representing XML documents with embedded function symbols. These games were introduced to model rewriting processes for intensional documents in the Active XML framework, where input documents are to be rewritten into a given target schema by calls to external services. This paper studies the setting where dependencies between inputs and outputs of service calls are modelled by transducers, which has not been examined previously. It defines transducer models operating on nested words and studies their properties, as well as the computational complexity of the winning problem for transducer-based context-free games in several scenarios. While the complexity of this problem is quite high in most settings (ranging from NP-complete to undecidable), some tractable restrictions are also identified.Comment: Extended version of MFCS 2016 conference pape

Visibly Pushdown Transducers with Well-nested Outputs

Visibly pushdown transducers (VPTs) are visibly pushdown automata extended with outputs. They have been introduced to model transformations of nested words, i.e. words with a call/return structure. When outputs are also structured and well nested words, VPTs are a natural formalism to express tree transformations evaluated in streaming. We prove the class of VPTs with well-nested outputs to be decidable in PTIME. Moreover, we show that this class is closed under composition and that its type-checking against visibly pushdown languages is decidable

Normalization of Sequential Top-Down Tree-to-Word Transducers

International audienceWe study normalization of deterministic sequential top-down tree-to-word transducers (STWs), that capture the class of deterministic top-down nested-word to word transducers. We identify the subclass of earliest STWs (eSTWs) that yield normal forms when minimized. The main result of this paper is an effective normalization procedure for STWs. It consists of two stages: we first convert a given STW to an equivalent eSTW, and then, we minimize the eSTW. Keywords: formal language theory, tree automata, transformations, XML databases, XSLTExtended Version: A long version is available here.</p

Tree Transducers and Formal Methods (Dagstuhl Seminar 13192)

The aim of this Dagstuhl Seminar was to bring together researchers from various research areas related to the theory and application of tree transducers. Recently, interest in tree transducers has been revived due to surprising new applications in areas such as XML databases, security verification, programming language theory, and linguistics. This seminar therefore aimed to inspire the exchange of theoretical results and information regarding the practical requirements related to tree transducers

Synthesis of recursive state machines from libraries of game modules

2013 - 2014This thesis is focused on synthesis. In formal veri cation synthesis can be referred to the controller synthesis and the system synthesis. This work combines both this area of research. First we focus on synthesizing modular controllers considering game on recursive game graph with the requirement that the strategy for the protagonist must be modular. A recursive game graph is composed of a set of modules, whose vertices can be standard vertices or can correspond to invocations of other modules and the standard and the set of vertices is split into two sets each controlled by one of the players. A strategy is modular if it is local to a module and is oblivious to previous module invocations, and thus does not depend on the context of invocation. We study for the rst time modular strategies with respect to winning conditions that can be expressed languages of pushdown automata. We show that pushdown modular games are undecidable in general, and become decidable for visibly pushdown automata speci cations. We carefully characterize the computational complexity of the considered decision problem. In particular, we show that modular games with a universal B uchi or co-B uchi visibly pushdown winning condition are Exptime-complete, and when the winning condition is given as a CaRet or Nwtl temporal logic formula the problem is 2Exptime-complete, and it remains 2Exptime-hard even for simple fragments of these logics. As a further contribution, we present a di erent synthesis algorithm that runs faster than known solutions for large speci cations and many exits. In the second part of this thesis, we introduce and solve a new componentbased synthesis problem that subsumes the synthesis from libraries of recursive components introduced by Lustig and Vardi with the modular synthesis introduced by Alur et al. for recursive game graphs. We model the components of our libraries as game modules of a recursive game graph with unmapped boxes, and consider as correctness speci cation a target set of vertices. To solve this problem, we give an exponential-time xed-point algorithm that computes annotations for the vertices of the library components by exploring them backwards. We show a matching lower-bound via a direct reduction from linear-space alternating Turing machines, thus proving Exptime-completeness. We also give a second algorithm that solves this problem by annotating in a table the result of many local reachability game queries on each game component. This algorithm is exponential only in the number of the exits of the game components, and thus shows that the problem is xed-parameter tractable. Finally, we study a more general synthesis problem for component-based pushdown systems, the modular synthesis from a library of components (Lms). We model each component as a game graph with boxes as placeholders for calls to components, as in the previous model, but now the library is equipped also with a box-to-component map that is a partial function from boxes to components. An instance of a component C is essentially a copy of C along with a local strategy that resolves the nondeterminism of pl 0. An RSM S synthesized from a library is a set of instances along with a total function that maps each box in S to an instance of S and is consistent with the box-to-component map of the library. We give a solution to the Lms problem with winning conditions given as internal reachability objectives, or as external deterministic nite automata (FA) and deterministic visibly pushdown automata (VPA) (6). We show that the Lms problem is Exptime-complete for any of the considered speci cations. [edited by Author]XIII n.s

The many facets of string transducers

Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem

Multi-weighted Automata Models and Quantitative Logics

Recently, multi-priced timed automata have received much attention for real-time systems. These automata extend priced timed automata by featuring several price parameters. This permits to compute objectives like the optimal ratio between rewards and costs. Arising from the model of timed automata, the multi-weighted setting has also attracted much notice for classical nondeterministic automata. The present thesis develops multi-weighted MSO-logics on finite, infinite and timed words which are expressively equivalent to multi-weighted automata, and studies decision problems for them. In addition, a Nivat-like theorem for weighted timed automata is proved; this theorem establishes a connection between quantitative and qualitative behaviors of timed automata. Moreover, a logical characterization of timed pushdown automata is given