5,473 research outputs found
Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis
In Boolean synthesis, we are given an LTL specification, and the goal is to
construct a transducer that realizes it against an adversarial environment.
Often, a specification contains both Boolean requirements that should be
satisfied against an adversarial environment, and multi-valued components that
refer to the quality of the satisfaction and whose expected cost we would like
to minimize with respect to a probabilistic environment.
In this work we study, for the first time, mean-payoff games in which the
system aims at minimizing the expected cost against a probabilistic
environment, while surely satisfying an -regular condition against an
adversarial environment. We consider the case the -regular condition is
given as a parity objective or by an LTL formula. We show that in general,
optimal strategies need not exist, and moreover, the limit value cannot be
approximated by finite-memory strategies. We thus focus on computing the
limit-value, and give tight complexity bounds for synthesizing
-optimal strategies for both finite-memory and infinite-memory
strategies.
We show that our game naturally arises in various contexts of synthesis with
Boolean and multi-valued objectives. Beyond direct applications, in synthesis
with costs and rewards to certain behaviors, it allows us to compute the
minimal sensing cost of -regular specifications -- a measure of quality
in which we look for a transducer that minimizes the expected number of signals
that are read from the input
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Computations by fly-automata beyond monadic second-order logic
We present logically based methods for constructing XP and FPT graph
algorithms, parametrized by tree-width or clique-width. We will use
fly-automata introduced in a previous article. They make possible to check
properties that are not monadic second-order expressible because their states
may include counters, so that their sets of states may be infinite. We equip
these automata with output functions, so that they can compute values
associated with terms or graphs. Rather than new algorithmic results we present
tools for constructing easily certain dynamic programming algorithms by
combining predefined automata for basic functions and properties.Comment: Accepted for publication in Theoretical Computer Scienc
Efficient Algorithms for Morphisms over Omega-Regular Languages
Morphisms to finite semigroups can be used for recognizing omega-regular
languages. The so-called strongly recognizing morphisms can be seen as a
deterministic computation model which provides minimal objects (known as the
syntactic morphism) and a trivial complementation procedure. We give a
quadratic-time algorithm for computing the syntactic morphism from any given
strongly recognizing morphism, thereby showing that minimization is easy as
well. In addition, we give algorithms for efficiently solving various decision
problems for weakly recognizing morphisms. Weakly recognizing morphism are
often smaller than their strongly recognizing counterparts. Finally, we
describe the language operations needed for converting formulas in monadic
second-order logic (MSO) into strongly recognizing morphisms, and we give some
experimental results.Comment: Full version of a paper accepted to FSTTCS 201
LTLf/LDLf Non-Markovian Rewards
In Markov Decision Processes (MDPs), the reward obtained in a state is Markovian, i.e., depends on the last state and action. This dependency makes it difficult to reward more interesting long-term behaviors, such as always closing a door after it has been opened, or providing coffee only following a request. Extending MDPs to handle non-Markovian reward functions was the subject of two previous lines of work. Both use LTL variants to specify the reward function and then compile the new model back into a Markovian model. Building on recent progress in temporal logics over finite traces, we adopt LDLf for specifying non-Markovian rewards and provide an elegant automata construction for building a Markovian model, which extends that of previous work and offers strong minimality and compositionality guarantees
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