1,423 research outputs found
Refinement Modal Logic
In this paper we present {\em refinement modal logic}. A refinement is like a
bisimulation, except that from the three relational requirements only `atoms'
and `back' need to be satisfied. Our logic contains a new operator 'all' in
addition to the standard modalities 'box' for each agent. The operator 'all'
acts as a quantifier over the set of all refinements of a given model. As a
variation on a bisimulation quantifier, this refinement operator or refinement
quantifier 'all' can be seen as quantifying over a variable not occurring in
the formula bound by it. The logic combines the simplicity of multi-agent modal
logic with some powers of monadic second-order quantification. We present a
sound and complete axiomatization of multi-agent refinement modal logic. We
also present an extension of the logic to the modal mu-calculus, and an
axiomatization for the single-agent version of this logic. Examples and
applications are also discussed: to software verification and design (the set
of agents can also be seen as a set of actions), and to dynamic epistemic
logic. We further give detailed results on the complexity of satisfiability,
and on succinctness
Generating and Solving Symbolic Parity Games
We present a new tool for verification of modal mu-calculus formulae for
process specifications, based on symbolic parity games. It enhances an existing
method, that first encodes the problem to a Parameterised Boolean Equation
System (PBES) and then instantiates the PBES to a parity game. We improved the
translation from specification to PBES to preserve the structure of the
specification in the PBES, we extended LTSmin to instantiate PBESs to symbolic
parity games, and implemented the recursive parity game solving algorithm by
Zielonka for symbolic parity games. We use Multi-valued Decision Diagrams
(MDDs) to represent sets and relations, thus enabling the tools to deal with
very large systems. The transition relation is partitioned based on the
structure of the specification, which allows for efficient manipulation of the
MDDs. We performed two case studies on modular specifications, that demonstrate
that the new method has better time and memory performance than existing PBES
based tools and can be faster (but slightly less memory efficient) than the
symbolic model checker NuSMV.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
Temporal Stream Logic: Synthesis beyond the Bools
Reactive systems that operate in environments with complex data, such as
mobile apps or embedded controllers with many sensors, are difficult to
synthesize. Synthesis tools usually fail for such systems because the state
space resulting from the discretization of the data is too large. We introduce
TSL, a new temporal logic that separates control and data. We provide a
CEGAR-based synthesis approach for the construction of implementations that are
guaranteed to satisfy a TSL specification for all possible instantiations of
the data processing functions. TSL provides an attractive trade-off for
synthesis. On the one hand, synthesis from TSL, unlike synthesis from standard
temporal logics, is undecidable in general. On the other hand, however,
synthesis from TSL is scalable, because it is independent of the complexity of
the handled data. Among other benchmarks, we have successfully synthesized a
music player Android app and a controller for an autonomous vehicle in the Open
Race Car Simulator (TORCS.
Limit Your Consumption! Finding Bounds in Average-energy Games
Energy games are infinite two-player games played in weighted arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. Here, we consider the problem of determining upper bounds on the
average accumulated energy or on the capacity while satisfying a given lower
bound, i.e., we do not determine whether a given bound is sufficient to meet
the specification, but if there exists a sufficient bound to meet it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
Uniform Strategies
We consider turn-based game arenas for which we investigate uniformity
properties of strategies. These properties involve bundles of plays, that arise
from some semantical motive. Typically, we can represent constraints on allowed
strategies, such as being observation-based. We propose a formal language to
specify uniformity properties and demonstrate its relevance by rephrasing
various known problems from the literature. Note that the ability to correlate
different plays cannot be achieved by any branching-time logic if not equipped
with an additional modality, so-called R in this contribution. We also study an
automated procedure to synthesize strategies subject to a uniformity property,
which strictly extends existing results based on, say standard temporal logics.
We exhibit a generic solution for the synthesis problem provided the bundles of
plays rely on any binary relation definable by a finite state transducer. This
solution yields a non-elementary procedure.Comment: (2012
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