Computing the bandwidth coefficient α for normal timed automata

Determine an algorithm that, given a normal timed automaton whose bandwidth scales as Θ(log(1/ε)) as ε→0, computes the coefficient α that multiplies log(1/ε) in the leading-order asymptotics of the ε-capacitive or ε-entropic bandwidth. The solution should handle the most general normal timed automata, beyond typical cases where α coincides with the number of continuous degrees of freedom per time unit in an optimal cycle.

Background

The paper classifies timed automata into three classes by bandwidth growth: meager (O(1)), normal (Θ(log(1/ε))), and obese (Θ(1/ε)). Prior work computed bandwidth for meager automata, and the present paper computes the leading 1/ε term for obese automata via an abstraction to weighted timed graphs.

For normal automata, the bandwidth behaves like α log(1/ε). In typical instances, α equals the number of continuous timing degrees of freedom per time unit along an optimal cycle, but a general method to compute α for arbitrary normal automata has not been established. The authors explicitly state that computing α in the most general case remains open.