Weighted automata are nondeterministic automata with numerical weights on
transitions. They can define quantitative languages~$L$ that assign to each
word~$w$ a real number~$L(w)$. In the case of infinite words, the value of a
run is naturally computed as the maximum, limsup, liminf, limit-average, or
discounted-sum of the transition weights. The value of a word $w$ is the
supremum of the values of the runs over $w$. We study expressiveness and
closure questions about these quantitative languages.
Gist is a tool that (a) solves the qualitative analysis problem of turn-based
probabilistic games with {\omega}-regular objectives; and (b) synthesizes
reasonable environment assumptions for synthesis of unrealizable
specifications. Our tool provides the first and efficient implementations of
several reduction-based techniques to solve turn-based probabilistic games, and
uses the analysis of turn-based probabilistic games for synthesizing
environment assumptions for unrealizable specifications.
Often one has a preference order among the different systems that satisfy a
given specification. Under a probabilistic assumption about the possible
inputs, such a preference order is naturally expressed by a weighted automaton,
which assigns to each word a value, such that a system is preferred if it
generates a higher expected value.
The standard procedure for hardware design consists of describing circuit in
a hardware description language at logic level followed by extensive
verification and logic-synthesis. However, this process consumes significant
time and needs a lot of effort. An alternative is to use formal specification
language as a high-level hardware description language and synthesize hardware
from formal specification. Bloem et.al. gave formal specifications and
synthesize the AMBA AHB Arbiter.
We study observation-based strategies for partially-observable Markov
decision processes (POMDPs) with omega-regular objectives. An observation-based
strategy relies on partial information about the history of a play, namely, on
the past sequence of observations. We consider the qualitative analysis
problem: given a POMDP with an omega-regular objective, whether there is an
observation-based strategy to achieve the objective with probability~1
(almost-sure winning), or with positive probability (positive winning). Our
main results are twofold.
Nondeterministic weighted automata are finite automata with numerical weights
on transitions. They define quantitative languages L that assign to each word w
a real number L(w). The value of an infinite word w is computed as the maximal
value of all runs over w, and the value of a run as the maximum, limsup,
liminf, limit average, or discounted sum of the transition weights. We
introduce probabilistic weighted automata, in which the transitions are chosen
in a randomized (rather than nondeterministic) fashion. Under almost-sure
semantics (resp.