137 research outputs found
Safe Schedulability of Bounded-Rate Multi-Mode Systems
Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch
freely among a finite set of modes, and whose dynamics is specified by a finite
number of real-valued variables with mode-dependent rates that can vary within
given bounded sets. The schedulability problem for BMMS is defined as an
infinite-round game between two players---the scheduler and the
environment---where in each round the scheduler proposes a time and a mode
while the environment chooses an allowable rate for that mode, and the state of
the system changes linearly in the direction of the rate vector. The goal of
the scheduler is to keep the state of the system within a pre-specified safe
set using a non-Zeno schedule, while the goal of the environment is the
opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS
where a winning strategy of the scheduler corresponds to a robust
energy-optimal policy. We present an algorithm to decide whether the scheduler
has a winning strategy from an arbitrary starting state, and give an algorithm
to compute such a winning strategy, if it exists. We show that the
schedulability problem for BMMS is co-NP complete in general, but for two
variables it is in PTIME. We also study the discrete schedulability problem
where the environment has only finitely many choices of rate vectors in each
mode and the scheduler can make decisions only at multiples of a given clock
period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201
First-order definable string transformations
The connection between languages defined by computational models and logic
for languages is well-studied. Monadic second-order logic and finite automata
are shown to closely correspond to each-other for the languages of strings,
trees, and partial-orders. Similar connections are shown for first-order logic
and finite automata with certain aperiodicity restriction. Courcelle in 1994
proposed a way to use logic to define functions over structures where the
output structure is defined using logical formulas interpreted over the input
structure. Engelfriet and Hoogeboom discovered the corresponding "automata
connection" by showing that two-way generalised sequential machines capture the
class of monadic-second order definable transformations. Alur and Cerny further
refined the result by proposing a one-way deterministic transducer model with
string variables---called the streaming string transducers---to capture the
same class of transformations. In this paper we establish a transducer-logic
correspondence for Courcelle's first-order definable string transformations. We
propose a new notion of transition monoid for streaming string transducers that
involves structural properties of both underlying input automata and variable
dependencies. By putting an aperiodicity restriction on the transition monoids,
we define a class of streaming string transducers that captures exactly the
class of first-order definable transformations.Comment: 31 page
FO-definable transformations of infinite strings
The theory of regular and aperiodic transformations of finite strings has
recently received a lot of interest. These classes can be equivalently defined
using logic (Monadic second-order logic and first-order logic), two-way
machines (regular two-way and aperiodic two-way transducers), and one-way
register machines (regular streaming string and aperiodic streaming string
transducers). These classes are known to be closed under operations such as
sequential composition and regular (star-free) choice; and problems such as
functional equivalence and type checking, are decidable for these classes. On
the other hand, for infinite strings these results are only known for
-regular transformations: Alur, Filiot, and Trivedi studied
transformations of infinite strings and introduced an extension of streaming
string transducers over -strings and showed that they capture monadic
second-order definable transformations for infinite strings. In this paper we
extend their work to recover connection for infinite strings among first-order
logic definable transformations, aperiodic two-way transducers, and aperiodic
streaming string transducers
Competitive optimisation on timed automata
Timed automata are finite automata accompanied by a finite set of real-valued variables called clocks. Optimisation problems on timed automata are fundamental to the verification of properties of real-time systems modelled as timed automata, while the control-program synthesis problem of such systems can be modelled as a two-player game. This thesis presents a study of optimisation problems and two-player games on timed automata under a general heading of competitive optimisation on timed automata.
This thesis views competitive optimisation on timed automata as a multi-stage decision process, where one or two players are confronted with the problem of choosing a sequence of timed moves—a time delay and an action—in order to optimise their objectives. A solution of such problems consists of the “optimal” value of the objective and an “optimal” strategy for each player. This thesis introduces a novel class of strategies, called boundary strategies, that suggest to a player a symbolic timed move of the form (b, c, a)— “wait until the value of the clock c is in very close proximity of the integer b, and then execute a transition labelled with the action a”. A distinctive feature of the competitive optimisation problems discussed in this thesis is the existence of optimal boundary strategies. Surprisingly perhaps, many competitive optimisation problems on timed automata of practical interest admit optimal boundary strategies. For example, optimisation problems with reachability price, discounted price, and average-price objectives, and two-player turn-based games with reachability time and average time objectives.
The existence of optimal boundary strategies allows one to work with a novel abstraction of timed automata, called a boundary region graph, where players can use only boundary strategies. An interesting property of a boundary region graph is that, for every state, the set of reachable states is finite. Hence, the existence of optimal boundary strategies permits us to reduce competitive optimisation problem on a timed automaton to the corresponding competitive optimisation problem on a finite graph
Revisiting Robustness in Priced Timed Games
Priced timed games are optimal-cost reachability games played between two
players---the controller and the environment---by moving a token along the
edges of infinite graphs of configurations of priced timed automata. The goal
of the controller is to reach a given set of target locations as cheaply as
possible, while the goal of the environment is the opposite. Priced timed games
are known to be undecidable for timed automata with or more clocks, while
they are known to be decidable for automata with clock.
In an attempt to recover decidability for priced timed games Bouyer, Markey,
and Sankur studied robust priced timed games where the environment has the
power to slightly perturb delays proposed by the controller. Unfortunately,
however, they showed that the natural problem of deciding the existence of
optimal limit-strategy---optimal strategy of the controller where the
perturbations tend to vanish in the limit---is undecidable with or more
clocks. In this paper we revisit this problem and improve our understanding of
the decidability of these games. We show that the limit-strategy problem is
already undecidable for a subclass of robust priced timed games with or
more clocks. On a positive side, we show the decidability of the existence of
almost optimal strategies for the same subclass of one-clock robust priced
timed games by adapting a classical construction by Bouyer at al. for one-clock
priced timed games
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