Alternating Finite Automata Research Articles

Operations on Boolean and Alternating Finite Automata

Operations on Boolean and Alternating Finite Automata

A Note on Cooperating Systems of One-Way Alternating Finite Automata with Only Universal States

A Note on Cooperating Systems of One-Way Alternating Finite Automata with Only Universal States

Engineering of An Assertion-based PSLSimple-Verilog Dynamic Verifier by Alternating Automata

Alternating Finite Automata (AFA) has linear space complexity in representing Linear-Time Temporal Logics. However, It is difficult to manipulate AFA in the run-time. In this paper, we focus on implementation methods to make alternating automata from static representation to run-time verification engines. 1) We have Directed Acyclic Graphs (DAG) represent all possible runs of a Local-variable-enhanced AFA (LAFA). The acceptance of universal choices is conditioned on successful synchronization of universal branches. 2) We encode states and local variables by symbolic approaches, and adopt historic trees in representing all possible parallel runs. The encoding enables multiple assignments to states and local variables in a configuration. By those methods, we are able to maintain the linear complexity of verification in both space and time.

On-line Monitoring of Metric Temporal Logic with Time-Series Constraints Using Alternating Finite Automata

On-line Monitoring of Metric Temporal Logic with Time-Series Constraints Using Alternating Finite Automata

Language equations for timed alternating finite automata

Traditionally, finite state automata are untimed or asynchronous models of computation in which only the ordering of events, not the time at which events occur, would affect the result of a computation. For real-time systems, it is important to augment these models of computation with a notion of time. For this purpose timed automata have become a powerful canonical model for describing timed behaviors and an effective tool for modeling real-time computations. In this paper, we extend the notion of timed alternating finite automata (TAFA), a class of alternating finite automata (AFA) extended with a finite set of real-valued clocks, and we present an algebraic interpretation of TAFA which parallels that of timed regular expressions and language equations. We further extend the equational representation of AFA to describe timed alternating finite automata, and explore solutions for such equations over time languages.

Efficient implementation of regular languages using reversed alternating finite automata

Alternating finite automata (AFA) provide a natural and succinct way to denote regular languages. We introduce a bit-wise representation of reversed AFA ( r-AFA) transition functions and describe an efficient implementation method for r-AFA and their operations using this representation. Experiments have shown that this implementation is much more efficient than, for instance, the Grail DFA implementation in both space and time.

Equations and regular-like expressions for afa

lternating finite automata are a generalization of non-deterministic finite automata and a mechanism that models parallel computation. It has been shown in [6] that alternating finite automata (AFA) have several theoretical properties and practical features. In this paper, we further study alternating finite automata. A new type of system of equations is introduced. The systems of equations to be considered involve Boolean expressions over a finite set X and the symbols of an alphabet A. Each AFA can be described as a system of equations that has a unique fixpoint, and whose solutions are precisely the regular languages. We present an algebraic interpretation of AFA, which parallels that of regular expressions and of linear equations. We also explore direct ways of solving such systems and generating equivalent AFA from regular expressions or even extended regular expressions.