10 research outputs found
From LTL and Limit-Deterministic B\"uchi Automata to Deterministic Parity Automata
Controller synthesis for general linear temporal logic (LTL) objectives is a
challenging task. The standard approach involves translating the LTL objective
into a deterministic parity automaton (DPA) by means of the Safra-Piterman
construction. One of the challenges is the size of the DPA, which often grows
very fast in practice, and can reach double exponential size in the length of
the LTL formula. In this paper we describe a single exponential translation
from limit-deterministic B\"uchi automata (LDBA) to DPA, and show that it can
be concatenated with a recent efficient translation from LTL to LDBA to yield a
double exponential, \enquote{Safraless} LTL-to-DPA construction. We also report
on an implementation, a comparison with the SPOT library, and performance on
several sets of formulas, including instances from the 2016 SyntComp
competition
One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata
We present a unified translation of LTL formulas into deterministic Rabin
automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi
automata. The translations yield automata of asymptotically optimal size
(double or single exponential, respectively). All three translations are
derived from one single Master Theorem of purely logical nature. The Master
Theorem decomposes the language of a formula into a positive boolean
combination of languages that can be translated into {\omega}-automata by
elementary means. In particular, Safra's, ranking, and breakpoint constructions
used in other translations are not needed
Semantic Labelling and Learning for Parity Game Solving in LTL Synthesis
We propose "semantic labelling" as a novel ingredient for solving games in
the context of LTL synthesis. It exploits recent advances in the automata-based
approach, yielding more information for each state of the generated parity game
than the game graph can capture. We utilize this extra information to improve
standard approaches as follows. (i) Compared to strategy improvement (SI) with
random initial strategy, a more informed initialization often yields a winning
strategy directly without any computation. (ii) This initialization makes SI
also yield smaller solutions. (iii) While Q-learning on the game graph turns
out not too efficient, Q-learning with the semantic information becomes
competitive to SI. Since already the simplest heuristics achieve significant
improvements the experimental results demonstrate the utility of semantic
labelling. This extra information opens the door to more advanced learning
approaches both for initialization and improvement of strategies
A Verified and Compositional Translation of LTL to Deterministic Rabin Automata
We present a formalisation of the unified translation approach from linear temporal logic (LTL) to omega-automata from [Javier Esparza et al., 2018]. This approach decomposes LTL formulas into "simple" languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction for deterministic Rabin automata (DRA). We extract from this particular instantiation an executable tool translating LTL to DRAs. To the best of our knowledge this is the first verified translation of LTL to DRAs that is proven to be double-exponential in the worst case which asymptotically matches the known lower bound
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
Alternative Automata-based Approaches to Probabilistic Model Checking
In this thesis we focus on new methods for probabilistic model checking (PMC) with linear temporal logic (LTL). The standard approach translates an LTL formula into a deterministic ω-automaton with a double-exponential blow up.
There are approaches for Markov chain analysis against LTL with exponential runtime, which motivates the search for non-deterministic automata with restricted forms of non-determinism that make them suitable for PMC. For MDPs, the approach via deterministic automata matches the double-exponential lower bound, but a practical application might benefit from approaches via non-deterministic automata.
We first investigate good-for-games (GFG) automata. In GFG automata one can resolve the non-determinism for a finite prefix without knowing the infinite suffix and still obtain an accepting run for an accepted word. We explain that GFG automata are well-suited for MDP analysis on a theoretic level, but our experiments show that GFG automata cannot compete with deterministic automata.
We have also researched another form of pseudo-determinism, namely unambiguity, where for every accepted word there is exactly one accepting run. We present a polynomial-time approach for PMC of Markov chains against specifications given by an unambiguous Büchi automaton (UBA). Its two key elements are the identification whether the induced probability is positive, and if so, the identification of a state set inducing probability 1.
Additionally, we examine the new symbolic Muller acceptance described in the Hanoi Omega Automata Format, which we call Emerson-Lei acceptance. It is a positive Boolean formula over unconditional fairness constraints. We present a construction of small deterministic automata using Emerson-Lei acceptance. Deciding, whether an MDP has a positive maximal probability to satisfy an Emerson-Lei acceptance, is NP-complete. This fact has triggered a DPLL-based algorithm for deciding positiveness