Automatic Verification of Recursive Procedures with One Integer Parameter

International audienceContext-free processes (BPA) have been used for dataflow analysis in recursive procedures with applications in optimizing compilers. We introduce a more refined model called BPA(Z) that can model not only recursive dependencies, but also the passing of an integer parameter to a subroutine. Moreover, this parameter can be tested against conditions expressible in Presburger arithmetic. This new and more expressive model can still be analyzed automatically. We define Z-input 1-CM, a new class of 1-counter machines that take integer numbers as input, to describe sets of configurations of BPA(Z). We show that the Post* (the set of successors) of a set of BPA(Z)-configurations described by a Z-input 1-CM can be effectively constructed. The Pre* (set of predecessors) of a regular set can be effectively constructed as well. However, the Pre* of a set described by a Z-input 1-CM cannot be represented by a Z-input 1-CM in general and has an undecidable membership problem. Then we develop a new temporal logic based on reversal-bounded counter machines (i.e. machines which use counters such that the change between increasing and decreasing mode of each counter is bounded that can be used to describe properties of BPA(Z) and show that the model-checking problem is decidable

In the Maze of Data Languages

In data languages the positions of strings and trees carry a label from a finite alphabet and a data value from an infinite alphabet. Extensions of automata and logics over finite alphabets have been defined to recognize data languages, both in the string and tree cases. In this paper we describe and compare the complexity and expressiveness of such models to understand which ones are better candidates as regular models

Reachability in pushdown register automata

We investigate reachability in pushdown automata over infinite alphabets. We show that, in terms of reachability/emptiness, these machines can be faithfully represented using only 3r elements of the alphabet, where r is the number of registers. We settle the complexity of associated reachability/emptiness problems. In contrast to register automata, the emptiness problem for pushdown register automata is EXPTIME-complete, independent of the register storage policy used. We also solve the global reachability problem by representing pushdown configurations with a special register automaton. Finally, we examine extensions of pushdown storage to higher orders and show that reachability is undecidable at order 2

Automatic Verification of Recursive Procedures with one Integer Parameter

Context-free processes (BPA) have been used for dataflow-analysis in recursive procedures with applications in optimizing compilers [6]. We introduce a more refined model called BPA(ZZ) that can model not only recursive dependencies, but also the passing of integer parameters to subroutines. Moreover, these parameters can be tested against conditions expressible in Presburger-arithmetic