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...

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 study two enumeration problems for up-down alternating trees, i.e., rooted labelled trees T , where the labels v1, v2, v3, . . . on every path starting at the root of T satisfy v1 < v2 > v3 < v4 > · · · . First we consider various tree families of interest in combinatorics (such as unordered, ordered, d-ary and Motzkin trees) and study the number Tn of different up-down alternating labelled ...

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 ...

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...

In program synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. When the system is open, then at each moment it reads input signals and writes output signals, which depend on the input signals and the history of the computation so far. The specification considers all possible input sequences. Thus, if the specification is linear, it should hold ...

The power of top-down tree transducers and tree-to-graph-to-tree transducers (tgt transducers) to compute translations between hyperedge-replacement algebras is investigated. It turns out that top-down tree transducers are too weak in many cases. Tgt transducers are shown to be more powerful.

The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique consists of modeling the behaviours of the timed system as graphs, and interpreting these graphs on tree terms by showing a bound on their tree-width. We then ...

We present a top-down approach to calorimeter clustering. An algorithm based on minimal spanning tree theory is described briefly. We present a top-down approach to calorimeter clustering. An algorithm based on minimal spanning tree theory is described briefly.