11 research outputs found
Comparator automata in quantitative verification
The notion of comparison between system runs is fundamental in formal
verification. This concept is implicitly present in the verification of
qualitative systems, and is more pronounced in the verification of quantitative
systems. In this work, we identify a novel mode of comparison in quantitative
systems: the online comparison of the aggregate values of two sequences of
quantitative weights. This notion is embodied by {\em comparator automata}
({\em comparators}, in short), a new class of automata that read two infinite
sequences of weights synchronously and relate their aggregate values.
We show that {aggregate functions} that can be represented with B\"uchi
automaton result in comparators that are finite-state and accept by the B\"uchi
condition as well. Such {\em -regular comparators} further lead to
generic algorithms for a number of well-studied problems, including the
quantitative inclusion and winning strategies in quantitative graph games with
incomplete information, as well as related non-decision problems, such as
obtaining a finite representation of all counterexamples in the quantitative
inclusion problem.
We study comparators for two aggregate functions: discounted-sum and
limit-average. We prove that the discounted-sum comparator is -regular
iff the discount-factor is an integer. Not every aggregate function, however,
has an -regular comparator. Specifically, we show that the language of
sequence-pairs for which limit-average aggregates exist is neither
-regular nor -context-free. Given this result, we introduce the
notion of {\em prefix-average} as a relaxation of limit-average aggregation,
and show that it admits -context-free comparators
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
Model Checking Strategies from Synthesis Over Finite Traces
The innovations in reactive synthesis from {\em Linear Temporal Logics over
finite traces} (LTLf) will be amplified by the ability to verify the
correctness of the strategies generated by LTLf synthesis tools. This motivates
our work on {\em LTLf model checking}. LTLf model checking, however, is not
straightforward. The strategies generated by LTLf synthesis may be represented
using {\em terminating} transducers or {\em non-terminating} transducers where
executions are of finite-but-unbounded length or infinite length, respectively.
For synthesis, there is no evidence that one type of transducer is better than
the other since they both demonstrate the same complexity and similar
algorithms.
In this work, we show that for model checking, the two types of transducers
are fundamentally different. Our central result is that LTLf model checking of
non-terminating transducers is \emph{exponentially harder} than that of
terminating transducers. We show that the problems are EXPSPACE-complete and
PSPACE-complete, respectively. Hence, considering the feasibility of
verification, LTLf synthesis tools should synthesize terminating transducers.
This is, to the best of our knowledge, the \emph{first} evidence to use one
transducer over the other in LTLf synthesis.Comment: Accepted by ATVA 2
LNCS
Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. Optimization is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the satisficing problem, where instead of searching for optimal solutions, the goal is to search for solutions that adhere to a given threshold bound.
This work defines and investigates the satisficing problem on a two-player graph game with the discounted-sum cost model. We show that while the satisficing problem can be solved using numerical methods just like the optimization problem, this approach does not render compelling benefits over optimization. When the discount factor is, however, an integer, we present another approach to satisficing, which is purely based on automata methods. We show that this approach is algorithmically more performant – both theoretically and empirically – and demonstrates the broader applicability of satisficing over optimization
Multi-Agent Systems with Quantitative Satisficing Goals
In the study of reactive systems, qualitative properties are usually easier
to model and analyze than quantitative properties. This is especially true in
systems where mutually beneficial cooperation between agents is possible, such
as multi-agent systems. The large number of possible payoffs available to
agents in reactive systems with quantitative properties means that there are
many scenarios in which agents deviate from mutually beneficial outcomes in
order to gain negligible payoff improvements. This behavior often leads to less
desirable outcomes for all agents involved. For this reason we study
satisficing goals, derived from a decision-making approach aimed at meeting a
good-enough outcome instead of pure optimization. By considering satisficing
goals, we are able to employ efficient automata-based algorithms to find
pure-strategy Nash equilibria. We then show that these algorithms extend to
scenarios in which agents have multiple thresholds, providing an approximation
of optimization while still retaining the possibility of mutually beneficial
cooperation and efficient automata-based algorithms. Finally, we demonstrate a
one-way correspondence between the existence of -equilibria and the
existence of equilibria in games where agents have multiple thresholds.Comment: Preliminary version of the technical report for a paper to appear in
IJCAI'2
Specification-Guided Learning of Nash Equilibria with High Social Welfare
Reinforcement learning has been shown to be an effective strategy for
automatically training policies for challenging control problems. Focusing on
non-cooperative multi-agent systems, we propose a novel reinforcement learning
framework for training joint policies that form a Nash equilibrium. In our
approach, rather than providing low-level reward functions, the user provides
high-level specifications that encode the objective of each agent. Then, guided
by the structure of the specifications, our algorithm searches over policies to
identify one that provably forms an -Nash equilibrium (with high
probability). Importantly, it prioritizes policies in a way that maximizes
social welfare across all agents. Our empirical evaluation demonstrates that
our algorithm computes equilibrium policies with high social welfare, whereas
state-of-the-art baselines either fail to compute Nash equilibria or compute
ones with comparatively lower social welfare
Synthesis from Satisficing and Temporal Goals
Reactive synthesis from high-level specifications that combine hard
constraints expressed in Linear Temporal Logic LTL with soft constraints
expressed by discounted-sum (DS) rewards has applications in planning and
reinforcement learning. An existing approach combines techniques from LTL
synthesis with optimization for the DS rewards but has failed to yield a sound
algorithm. An alternative approach combining LTL synthesis with satisficing DS
rewards (rewards that achieve a threshold) is sound and complete for integer
discount factors, but, in practice, a fractional discount factor is desired.
This work extends the existing satisficing approach, presenting the first sound
algorithm for synthesis from LTL and DS rewards with fractional discount
factors. The utility of our algorithm is demonstrated on robotic planning
domains