We propose an extension of visibly pushdown automata by means of weights (represented as positive integers) associated with transitions, called visibly pushdown automata with multiplicities. The multiplicity of a computation is the product of the multiplicities of the transitions used along this computation. The multiplicity of an input is the sum of the ones of all its successful computations....

Streaming validation and querying of XML documents are often based on automata for tree-like structures. We propose a new notion of streaming tree automata in order to unify the two main approaches, which have not been linked so far: automata for nested words or equivalently visibly pushdown automata, and respectively pushdown forest automata.

This paper presents a way to verify CCS (without renaming) specifications using tree regular model checking. From a term rewriting system and a tree automaton representing the semantics of CCS and equations of a CCS specification to analyse, an over-approximation of the set of reachable terms is computed from an initial configuration. This set, in the framework of CCS, represents an over-approx...

Given an NFA A = (Q,Σ, δ, s, F ) and word w = a1a2 . . . an, we can characterize when A accepts the word w as follows : Construct a tree of height n + 1. The root of the tree is labelled by s. If a node at level i, 1 ≤ i ≤ n, is labelled by a state q and δ(q, ai) = X then it has |X| children labelled by the elements of X. Now treat each internal node in this tree as the logical ∨ operator to ob...

Visibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdo...

Parikh’s game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone μ-calculus, which in turn is expressively equivalent to monotone modal automata. Parity games and automata are important tools for dealing with the combinatorial complexit...

While the μ-calculus notoriously subsumes Alternating-time Temporal Logic (ATL), we show that the epistemic μ-calculus does not subsume ATL with imperfect information (ATLi), for the synchronous perfect-recall semantics. To prove this we first establish that jumping parity tree automata (JTA), a recently introduced extension of alternating parity tree automata, are expressively equivalent to th...

We propose a realizability semantics for automata on infinite trees, based on categories of games built on usual simple games, and generalizing usual acceptance games of tree automata. Our approach can be summarized with the slogan “automata as objects, strategies as morphisms”. We show that the operations on tree automata used in the translations of MSOformulae to automata (underlying Rabin’s ...

We consider variants of alternating auxiliary stack automata and characterize their computational power when the number of alternations is bounded by a constant or unlimited. In this way we get new characterizations of NP, the polynomial hierarchy, PSpace, and bounded query classes like co-DP=NL〈NP[1]〉 and 2P=P , in a uniform framework. c © 2002 Elsevier Science B.V. All rights reserved.

It is proved that CTL+ is exponentially more succinct than CTL. More precisely, it is shown that every CTL formula (and every modal -calculus formula) equivalent to the CTL+ formula E(Fp0 ^ ^ Fpn 1) is of length at least n dn=2e , which is (2n=pn). This matches almost the upper bound provided by Emerson and Halpern, which says that for every CTL+ formula of length n there exists an equivalent C...