Verifying Recursive Active Documents with Positive Data Tree Rewriting

This paper proposes a data tree-rewriting framework for modeling evolving documents. The framework is close to Guarded Active XML, a platform used for handling XML repositories evolving through web services. We focus on automatic verification of properties of evolving documents that can contain data from an infinite domain. We establish the boundaries of decidability, and show that verification of a {\em positive} fragment that can handle recursive service calls is decidable. We also consider bounded model-checking in our data tree-rewriting framework and show that it is \nexptime-complete

Commutative Data Automata

Formalisms over infinite alphabets have recently received much focus in the community of the-oretical computer science. Data automata is a formal model for words over infinite alphabets proposed by Bojanczyk, Muscholl, Schwentick et. al. in 2006. A data automaton consists of two parts, a nondeterministic letter-to-letter transducer, and a class condition specified by a finite automaton over the output alphabet of the transducer, which acts as a condition on the subsequence of the outputs of the transducer in every class, namely, in every maximal set of po-sitions with the same data value. It is open whether the nonemptiness of data automata can be decided with elementary complexity. Very recently, a restriction of data automata with element-ary complexity, called weak data automata, was proposed by Kara, Schwentick and Tan and its nonemptiness problem was shown to be in 2-NEXPTIME. In weak data automata, the class condi-tions are specified by some simple constraints on the number of occurrences of labels occurring in every class. The aim of this paper is to demonstrate that the commutativity of class conditions is the genuine reason accounting for the elementary complexity of weak data automata. For this purpose, we define and investigate commutative data automata, which are data automata with class conditions restricted to commutative regular languages. We show that while the express-ive power of commutative data automata is strictly stronger than that of weak data automata, the nonemptiness problem of this model can still be decided with elementary complexity, more precisely, in 3-NEXPTIME. In addition, we extend the results to data ω-words and prove that the nonemptiness of commutative Büchi data automata can be decided in 4-NEXPTIME. We also provide logical characterizations for commutative (Büchi) data automata, similar to those for weak (Büchi) data automata

Register automata with linear arithmetic

We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RA-Q model allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits. The main feature of RA-Q is that despite the use of linear arithmetic, the so-called invariant problem---a generalization of the standard non-emptiness problem---is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RA-Q, commutativity and equivalence are polynomial-time inter-reducible with the invariant problem

Feasibility of Motion Planning on Acyclic and Strongly Connected Directed Graphs

Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem abstracting from geometric considerations. In this paper, we consider motion planning over directed graphs, which are of interest for asymmetric communication networks. Directed graphs generalize undirected graphs, while introducing a new source of complexity to the motion planning problem: moves are not reversible. We first consider the class of acyclic directed graphs and show that the feasibility can be solved in time linear in the product of the number of vertices and the number of arcs. We then turn to strongly connected directed graphs. We first prove a structural theorem for decomposing strongly connected directed graphs into strongly biconnected components.Based on the structural decomposition, we give an algorithm for the feasibility of motion planning on strongly connected directed graphs, and show that it can also be decided in time linear in the product of the number of vertices and the number of arcs.Comment: 19 pages, 9 figures, algorithm2e.st

Extending Temporal Logics with Data Variable Quantifications

Although data values are available in almost every computer system, reasoning about them is a challenging task due to the huge data size or even infinite data domains. Temporal logics are the well-known specification formalisms for reactive and concurrent systems. Various extensions of temporal logics have been proposed to reason about data values, mostly in the last decade. Among them, one natural idea is to extend temporal logics with variable quantifications ranging over an infinite data domain. In this paper, we focus on the variable extensions of two widely used temporal logics, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). Grumberg, Kupferman and Sheinvald recently investigated the extension of LTL with variable quantifications. They defined the extension as formulas in the prenex normal form, that is, all the variable quantifications precede the LTL formulas. Our goal in this paper is to do a relatively complete investigation on this topic. For this purpose, we define the extensions of LTL and CTL by allowing arbitrary nestings of variable quantifications, Boolean and temporal operators (the resulting logics are called respectively variable-LTL, in brief VLTL, and variable-CTL, in brief VCTL), and identify the decidability frontiers of both the satisfiability and model checking problem. In particular, we obtain the following results: 1) Existential variable quantifiers or one single universal quantifier in the beginning already entails undecidability for the satisfiability problem of both VLTL and VCTL, 2) If only existential path quantifiers are used in VCTL, then the satisfiability problem is decidable, no matter which variable quantifiers are available. 3) For VLTL formulas with one single universal variable quantifier in the beginning, if the occurrences of the non-parameterized atomic propositions are guarded by the positive occurrences of the quantified variable, then its satisfiability problem becomes decidable. Based on these results of the satisfiability problem, we deduce the (un)decidability results of the model checking problem