The reachability analysis of recursive programs that communicate asynchronously over reliable Fifo channels calls for restrictions to ensure decidability. Our first result characterizes communication topologies with a decidable reachability problem restricted to eager runs (i.e., runs where messages are either received immediately after being sent, or never received). The problem is ExpTime-com...

The paradigm of Computing by Observing, so far used for generating and accepting languages, is extended to transductions. We show that only string-rewriting rules of the form a→ b suffice to compute most rational and pushdown relations. Only pairs with empty left-hand side cause problems. Even non-pushdown relations can be computed, namely a test for prime numbers can be implemented.

We analyze the relationship between three ways of generating trees using collapsible pushdown systems (CPS’s): using deterministic CPS’s, nondeterministic CPS’s, and deterministic wordaccepting CPS’s. We prove that (for each level of the CPS and each input alphabet) the three classes of trees are equal. The nontrivial translations increase n− 1 times exponentially the size of the level-n CPS. T...

We prove undecidability of the problem whether a given pair of pushdown processes is weakly bisimilar. We also show that this undecidability result extends to a subclass of pushdown processes satisfying the normedness condition.

The emptiness of the intersection of visibly pushdown languages [1] is decidable. However, if different alphabet partitions, or more precisely pushdown alphabets, are considered, the emptiness of this intersection becomes undecidable. It will be shown that this problem can be split into four cases. One of them has already been studied, another one is trivial. Of the last two cases one will be p...

A stack is a last-in first-out sorting device with push and pop operations. Knuth [7] showed that a permutation π can be sorted (meaning that by applying push and pop operations to the sequence of entries π(1), . . . , π(n) we can output the sequence 1, . . . , n) if and only if π avoids the permutation 231, i.e., if and only if there do not exist three indices 1 ≤ i1 < i2 < i3 ≤ n such that π(...

We present a method to define unary relations P1, . . . , Pn such that the Monadic Second-Order theory of the natural integers endowed with the successor relation and P1, . . . , Pn is decidable. The main tool is a novel class of iterated pushdown automata whose transitions are controlled by tests on the store.

We consider infinite two-player games parametrized by a set P of natural numbers where the winning condition is given by a regular ω-language (including the parameter P ). Extending recent work of Rabinovich we study here predicates P where the structure (N,+1, P ) belongs to the pushdown hierarchy (or “Caucal hierarchy”). For such a predicate P where (N,+1, P ) occurs in the k-th level of the ...

In this paper, we study the program-point reachability problem of con-current pushdown systems that communicate asynchronously via unbounded andunordered message buffers. Our goal is to relax the common restriction that mes-sages can only be retrieved by a pushdown process when its stack is empty. Weintroduce a new class of asynchronously communicating pushdown systems witha...

In this paper, we address the verification problem of ordered multi-pushdown systems: A multistack extension of pushdown systems that comes with a constraint on stack operations such that a pop can only be performed on the first non-empty stack. First, we show that for an ordered multi-pushdown system the set of all predecessors of a regular set of configurations is an effectively constructible...