Logical reliability of interacting real-time tasks

Abstract

We propose the notion of logical reliability for real-time program tasks that interact through periodically updated program variables. We describe a reliability analysis that checks if the given short-term (e.g., single-period) reliability of a program variable update in an implementation is sufficient to meet the logical reliability requirement (of the program variable) in the long run. We then present a notion of design by refinement where a task can be refined by another task that writes to program variables with less logical reliability. The resulting analysis can be combined with an incremental schedulability analysis for interacting real-time tasks proposed earlier for the Hierarchical Timing Language (HTL), a coordination language for distributed real-time systems. We implemented a logical-reliabilityenhanced prototype of the compiler and runtime infrastructure for HTL.

Expressiveness and Closure Properties for Quantitative Languages

“…For example, peak power consumption can be modeled as the maximum of a sequence of weights representing power usage; energy use can be modeled as the sum; average response time as the limit average [1,2]. Quantitative languages can also be used to specify and verify reliability requirements: if a spe-cial symbol ⊥ is used to denote failure and has weight 1, while the other symbols have weight 0, one can use a limit-average automaton to specify a bound on the rate of failure in the long run [6]. The discounted sum can be used to specify that failures happening later are less important than those happening soon [10].…”

Mean-Payoff Automaton Expressions

“…While nondeterministic LimInfAvgand LimSupAvg-automata are closed under the max operation, they are not closed under min and complement [5]. Alternating LimInfAvgand LimSupAvg-automata 6 are closed under max and min, but are not closed under complementation and sum [4] We define a robust class of quantitative languages for mean-payoff automata which is closed under max, min, sum, and complement, and which can express all natural examples of quantitative languages defined using the mean-payoff measure [1,5,6].…”

“…We show that (a) all decision problems (quantitative emptiness, universality, inclusion, and equivalence) are decidable for mean-payoff automaton expressions; (b) mean-payoff automaton expressions are incomparable in expressive power with both the nondeterministic and alternating mean-payoff automata (i.e., there are quantitative languages expressible by mean-payoff automaton expressions that are not expressible by alternating mean-payoff automata, and there are quantitative languages expressible by nondeterministic mean-payoff automata that are not expressible by mean-payoff automata expressions); and (c) the properties of cut-point languages (i.e., the sets of words with value above a certain threshold) for deterministic automata carry over to mean-payoff automaton expressions, mainly the cut-point language is ωregular when the threshold is isolated (i.e., some neeighborhood around the threshold contains no word). Moreover, mean-payoff automaton expressions can express all examples in the literature of quantitative properties using mean-payoff measure [1,5,6]. Along with the quantitative generalization of the classical decision problems, we also consider the notion of distance between two quantitative languages L A and L B , defined as sup w |L A (w)−L B (w)|.…”