323,264 research outputs found
Quasipolynomial Set-Based Symbolic Algorithms for Parity Games
Solving parity games, which are equivalent to modal -calculus model
checking, is a central algorithmic problem in formal methods. Besides the
standard computation model with the explicit representation of games, another
important theoretical model of computation is that of set-based symbolic
algorithms. Set-based symbolic algorithms use basic set operations and one-step
predecessor operations on the implicit description of games, rather than the
explicit representation. The significance of symbolic algorithms is that they
provide scalable algorithms for large finite-state systems, as well as for
infinite-state systems with finite quotient. Consider parity games on graphs
with vertices and parity conditions with priorities. While there is a
rich literature of explicit algorithms for parity games, the main results for
set-based symbolic algorithms are as follows: (a) an algorithm that requires
symbolic operations and symbolic space; and (b) an improved
algorithm that requires symbolic operations and symbolic
space. Our contributions are as follows: (1) We present a black-box set-based
symbolic algorithm based on the explicit progress measure algorithm. Two
important consequences of our algorithm are as follows: (a) a set-based
symbolic algorithm for parity games that requires quasi-polynomially many
symbolic operations and symbolic space; and (b) any future improvement
in progress measure based explicit algorithms imply an efficiency improvement
in our set-based symbolic algorithm for parity games. (2) We present a
set-based symbolic algorithm that requires quasi-polynomially many symbolic
operations and symbolic space. Moreover, for the important
special case of , our algorithm requires only polynomially many
symbolic operations and poly-logarithmic symbolic space.Comment: Published at LPAR-22 in 201
Estimating good discrete partitions from observed data: symbolic false nearest neighbors
A symbolic analysis of observed time series data requires making a discrete
partition of a continuous state space containing observations of the dynamics.
A particular kind of partition, called ``generating'', preserves all dynamical
information of a deterministic map in the symbolic representation, but such
partitions are not obvious beyond one dimension, and existing methods to find
them require significant knowledge of the dynamical evolution operator or the
spectrum of unstable periodic orbits. We introduce a statistic and algorithm to
refine empirical partitions for symbolic state reconstruction. This method
optimizes an essential property of a generating partition: avoiding topological
degeneracies. It requires only the observed time series and is sensible even in
the presence of noise when no truly generating partition is possible. Because
of its resemblance to a geometrical statistic frequently used for
reconstructing valid time-delay embeddings, we call the algorithm ``symbolic
false nearest neighbors''
Integrating Abstract Caches with Symbolic Pipeline Analysis
Static worst-case execution time analysis of real-time tasks is based on abstract models that capture the timing behavior of the processor on which the tasks run. For complex processors, task-level execution time bounds are obtained by a state space exploration which involves the abstract model and the program. Partial state space exploration is not sound. Symbolic methods using binary decision diagrams (BDDs) allow for a full state space exploration of the pipeline, thereby maintaining soundness. Caches are too large to admit an efficient BDD representation. On the other hand, invariants of the cache state can be computed efficiently using abstract interpretation. How to integrate abstract caches with symbolic-state pipeline analysis is an open question. We propose a semi-symbolic domain to solve this problem. Statistical data from industrial-level software and WCET tools indicate that this new domain will enable an efficient analysis
Hybrid Compositional Reasoning for Reactive Synthesis from Finite-Horizon Specifications
LTLf synthesis is the automated construction of a reactive system from a
high-level description, expressed in LTLf, of its finite-horizon behavior. So
far, the conversion of LTLf formulas to deterministic finite-state automata
(DFAs) has been identified as the primary bottleneck to the scalabity of
synthesis. Recent investigations have also shown that the size of the DFA state
space plays a critical role in synthesis as well.
Therefore, effective resolution of the bottleneck for synthesis requires the
conversion to be time and memory performant, and prevent state-space explosion.
Current conversion approaches, however, which are based either on
explicit-state representation or symbolic-state representation, fail to address
these necessities adequately at scale: Explicit-state approaches generate
minimal DFA but are slow due to expensive DFA minimization. Symbolic-state
representations can be succinct, but due to the lack of DFA minimization they
generate such large state spaces that even their symbolic representations
cannot compensate for the blow-up.
This work proposes a hybrid representation approach for the conversion. Our
approach utilizes both explicit and symbolic representations of the
state-space, and effectively leverages their complementary strengths. In doing
so, we offer an LTLf to DFA conversion technique that addresses all three
necessities, hence resolving the bottleneck. A comprehensive empirical
evaluation on conversion and synthesis benchmarks supports the merits of our
hybrid approach.Comment: Accepted by AAAI 2020. Tool Lisa for (a). LTLf to DFA conversion, and
(b). LTLf synthesis can be found here: https://github.com/vardigroup/lis
Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives
Given a model and a specification, the fundamental model-checking problem
asks for algorithmic verification of whether the model satisfies the
specification. We consider graphs and Markov decision processes (MDPs), which
are fundamental models for reactive systems. One of the very basic
specifications that arise in verification of reactive systems is the strong
fairness (aka Streett) objective. Given different types of requests and
corresponding grants, the objective requires that for each type, if the request
event happens infinitely often, then the corresponding grant event must also
happen infinitely often. All -regular objectives can be expressed as
Streett objectives and hence they are canonical in verification. To handle the
state-space explosion, symbolic algorithms are required that operate on a
succinct implicit representation of the system rather than explicitly accessing
the system. While explicit algorithms for graphs and MDPs with Streett
objectives have been widely studied, there has been no improvement of the basic
symbolic algorithms. The worst-case numbers of symbolic steps required for the
basic symbolic algorithms are as follows: quadratic for graphs and cubic for
MDPs. In this work we present the first sub-quadratic symbolic algorithm for
graphs with Streett objectives, and our algorithm is sub-quadratic even for
MDPs. Based on our algorithmic insights we present an implementation of the new
symbolic approach and show that it improves the existing approach on several
academic benchmark examples.Comment: Full version of the paper. To appear in CAV 201
Conformant Planning via Symbolic Model Checking
We tackle the problem of planning in nondeterministic domains, by presenting
a new approach to conformant planning. Conformant planning is the problem of
finding a sequence of actions that is guaranteed to achieve the goal despite
the nondeterminism of the domain. Our approach is based on the representation
of the planning domain as a finite state automaton. We use Symbolic Model
Checking techniques, in particular Binary Decision Diagrams, to compactly
represent and efficiently search the automaton. In this paper we make the
following contributions. First, we present a general planning algorithm for
conformant planning, which applies to fully nondeterministic domains, with
uncertainty in the initial condition and in action effects. The algorithm is
based on a breadth-first, backward search, and returns conformant plans of
minimal length, if a solution to the planning problem exists, otherwise it
terminates concluding that the problem admits no conformant solution. Second,
we provide a symbolic representation of the search space based on Binary
Decision Diagrams (BDDs), which is the basis for search techniques derived from
symbolic model checking. The symbolic representation makes it possible to
analyze potentially large sets of states and transitions in a single
computation step, thus providing for an efficient implementation. Third, we
present CMBP (Conformant Model Based Planner), an efficient implementation of
the data structures and algorithm described above, directly based on BDD
manipulations, which allows for a compact representation of the search layers
and an efficient implementation of the search steps. Finally, we present an
experimental comparison of our approach with the state-of-the-art conformant
planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems
from the distribution packages of these systems, plus other problems defined to
stress a number of specific factors. Our approach appears to be the most
effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all
the problems where a comparison is possible, CMBP outperforms its competitors,
sometimes by orders of magnitude
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