Arden’s Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton.

Current implementations of Java make security decisions by searching the runtime call stack. These systems have attractive security properties, but they have been criticized as being dependent on specific artifacts of the Java implementation. This paper models the stack inspection algorithm in terms of a well-understood logic for access control and demonstrates how stack inspection is a useful ...

We propose a construction that augments the precomputation step of a regular tree pattern matching algorithm to include cost analysis. The matching device generated is a pushdown automaton in contrast with the conventionally generated tree pattern matching automaton. Our technique can handle a larger class of cost augmented regular tree grammars than can be preprocessed by conventional methods,...

A new and simple method for target code selection by tilling an abstract syntax tree is presented. As it is usual, tree patterns corresponding to target machine instructions are matched in the abstract syntax tree. Matching tree patterns is performed with the use of tree pattern pushdown automaton, which accepts all tree patterns matching the abstract syntax tree in the linear postfix bar notat...

Higher-order pushdown systems extend the idea of pushdown systems by using a “higher-order stack” (which is a nested stack). More precisely on level 1 this is a standard stack, on level 2 it is a stack of stacks, and so on. We study the higher-order pushdown systems in the context of infinite regular games. In the first part, we present a k-ExpTime algorithm to compute global positional winning...

We propose a practical technique to compile pattern-matching for prioritised overlapping patterns in equational languages into a minimal, deterministic, left-toright, matching automaton. First, we present a method for constructing a tree matching automaton for such patterns. This allows pattern-matching to be performed without any backtracking. Space requirements are reduced by using a directed...

Checking for language containment between nondeterministic ω-automata is a central task in automata-based hierarchical verification. We present a symbolic procedure for language containment checking between two Büchi automata. Our algorithm avoids determinization by intersecting the implementation automaton with the complement of the specification automaton as an alternating automaton. We prese...

Trees can be conveniently compressed with linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars which are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). It is shown that every linear straight-line context-free tree grammar can be transformed in polynomial ti...

Alternating automata have been commonly used as a basis for static verification of reactive systems. In this paper we show how alternating automata can be used in runtime verification. We present three algorithms to check at runtime whether a reactive program satisfies a temporal specification, expressed by a lineartime temporal logic formula. The three methods start from the same alternating a...