Partial-order methods make it possible to check properties of a concurrent system by state-space exploration without considering all interleavings of independent concurrent events. They have been applied to linear-time model checking, but so far only limited results are known about their applicability to branching-time model checking. In this paper, we introduce a general technique for lifting ...

Over the last few years, the automata-theoretic approach to realizability checking and synthesis of reactive modules, developed by Pnueli and Rosner, by Abadi, Lamport, and Wolper, and by Dill and Wong-Toi, has been quite successful, handling both the synchronous and the asynchronous cases. In this approach one transforms the specification into a tree automaton. The specification is realizable ...

A formula from monadic second order (mso) logic with one free variable can be used to deene a property of the nodes of a tree. Similarly, an mso formula with two free variables can be used to deene a binary relation between the nodes of a tree. It is proved that a node relation is mso deenable ii it can be computed by a nite-state tree-walking automaton, provided the automaton can test mso deen...

This paper presents a formal methodology for attack modeling and detection for networks. Our approach has three phases. First, we extend the basic attack tree approach [1] to capture (i) the temporal dependencies between components, and (ii) the expiration of an attack. Second, using the enhanced attack trees (EAT) we build a tree automaton that accepts a sequence of actions from input stream i...

A classical result by Rabin states that if a set of trees and its complement are both Büchi definable in the monadic second order logic, then these sets are weakly definable. In the language of -calculi, this theorem asserts the equality between the complexity classes 2 ∩ 2 and Comp( 1, 1) of the fixed-point alternation-depth hierarchy of the -calculus of tree languages. It is natural to ask wh...

Trees are one of the fundamental data structures used in Computer Science. We present a new kind of acyclic pushdown automata, the tree pattern pushdown automaton and the nonlinear tree pattern pushdown automaton, constructed for an ordered tree. These automata accept all tree patterns and nonlinear tree patterns, respectively, which match the tree and represent a full index of the tree for suc...

Ong has shown that the modal mu-calculus model checking problem (equivalently, the alternating parity tree automaton (APT) acceptance problem) of possibly-infinite ranked trees generated by order-n recursion schemes is n-EXPTIME complete. We consider two subclasses of APT and investigate the complexity of the respective acceptance problems. The main results are that, for APT with a single prior...

In this paper we provide an automaton-based solution to the decision problem for a large set of monadic second-order theories of deterministic tree structures. We achieve it in two steps: first, we reduce the considered problem to the problem of determining, for any Rabin tree automaton, whether it accepts a given tree; then, we exploit a suitable notion of tree equivalence to reduce (a number ...

The tree automaton completion is an algorithm used for proving safety properties on systems which can be modeled by a term rewriting system. This representation and verification technique works well for proving properties on infinite systems like cryptographic protocols or more recently on Java Bytecode programs. This algorithm computes a tree automaton which represents a (regular) over approxi...

In order for neural networks to learn complex languages or grammars, they must have sufficient computational power or resources to recognize or generate such languages. Though many approaches have been discussed, one obvious approach to enhancing the processing power of a recurrent neural network is to couple it with an external stack memory in effect creating a neural network pushdown automata...