We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure which can be seen as a nested stack of stacks. Our main result is that, for any higher-order context-free process, the set of all predecessors of a given regular set of configurations is regular and effectively constructible. This result generalizes the analogous result which is known for level 1 context-free processes. We show that this result holds also in the case of backward reachability analysis under a regular constraint on configurations. As a corollary, we obtain a symbolic model checking algorithm for the temporal logic E(U, X) with regular atomic predicates, i.e., the fragment of CTL restricted to the EU and EX modalities.We denote by O n the set of operations consisting of:We say that operation o is of level n, written l(o) = n, if o is either push n or pop n , or push w 1 if n = 1. We can now define the model studied in this paper. Definition 2.2. A higher-order context-free process of level n (or n-HCFP) is a pair H = (Γ, ∆), where Γ is a finite alphabet and ∆ ∈ Γ × O n is a finite set of transitions. A configuration of H is a n-store over Γ . H defines a transition relation ֒→ H between n-stores (or ֒→ when H is clear from the context), where s ֒→ H s ′ ⇐⇒ ∃(a, o) ∈ ∆ such that top 1 (s) = a and s ′ = o(s).The level l(d) of a transition d = (a, o) is simply the level of o. Let us give a few more notations concerning HCFP computations. Let H = (Γ, ∆) be a n-HCFP. A run of H starting from some store s 0 is a sequence s 0 s 1 s 2 . . . such that for all i ≥ 0, s i ֒→ s i+1 . The reflexive and transitive closure of ֒→ is written * ֒→ and called the reachability relation. For a given set C of n-stores, we also define the constrained transition relation ֒→ C = ֒→ ∩ (C × C), and its reflexive and transitive closure * ֒→ C . Now for any set of n-stores S, we consider the sets:By Lemma A.6, this implies that ∀s ′′ , t · s ′′ * ֒→ s ′′ , and in particular t · s

The original publication is available at ieeexplore.ieee.org.International audienceThis paper presents a quantitative extension for the linear-time temporal logic LTL allowing to specify the number of states satisfying certain sub-formulas along paths. We give decision procedures for the satisfiability and model checking of this new temporal logic and study the complexity of the corresponding problems. Furthermore we show that the problems become undecidable when more expressive constraints are considered

In this paper we consider parity games defined by higher-order pushdown automata. These automata generalise pushdown automata by the use of higher-order stacks, which are nested "stack of stacks" structures. Representing higher-order stacks as well-bracketed words in the usual way, we show that the winning regions of these games are regular sets of words. Moreover a finite automaton recognising this region can be effectively computed.A novelty of our work are abstract pushdown processes which can be seen as (ordinary) pushdown automata but with an infinite stack alphabet. We use the device to give a uniform presentation of our results.From our main result on winning regions of parity games we derive a solution to the Modal Mu-Calculus Global Model-Checking Problem for higher-order pushdown graphs as well as for ranked trees generated by higher-order safe recursion schemes.