120 research outputs found
Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs
Computing reachability probabilities is a fundamental problem in the analysis
of probabilistic programs. This paper aims at a comprehensive and comparative
account on various martingale-based methods for over- and under-approximating
reachability probabilities. Based on the existing works that stretch across
different communities (formal verification, control theory, etc.), we offer a
unifying account. In particular, we emphasize the role of order-theoretic fixed
points---a classic topic in computer science---in the analysis of probabilistic
programs. This leads us to two new martingale-based techniques, too. We give
rigorous proofs for their soundness and completeness. We also make an
experimental comparison using our implementation of template-based synthesis
algorithms for those martingales
A Component-oriented Framework for Autonomous Agents
The design of a complex system warrants a compositional methodology, i.e.,
composing simple components to obtain a larger system that exhibits their
collective behavior in a meaningful way. We propose an automaton-based paradigm
for compositional design of such systems where an action is accompanied by one
or more preferences. At run-time, these preferences provide a natural fallback
mechanism for the component, while at design-time they can be used to reason
about the behavior of the component in an uncertain physical world. Using
structures that tell us how to compose preferences and actions, we can compose
formal representations of individual components or agents to obtain a
representation of the composed system. We extend Linear Temporal Logic with two
unary connectives that reflect the compositional structure of the actions, and
show how it can be used to diagnose undesired behavior by tracing the
falsification of a specification back to one or more culpable components
Satisfiability of ECTL* with tree constraints
Recently, we have shown that satisfiability for with
constraints over is decidable using a new technique. This approach
reduces the satisfiability problem of with constraints over
some structure A (or class of structures) to the problem whether A has a
certain model theoretic property that we called EHD (for "existence of
homomorphisms is decidable"). Here we apply this approach to concrete domains
that are tree-like and obtain several results. We show that satisfiability of
with constraints is decidable over (i) semi-linear orders
(i.e., tree-like structures where branches form arbitrary linear orders), (ii)
ordinal trees (semi-linear orders where the branches form ordinals), and (iii)
infinitely branching trees of height h for each fixed . We
prove that all these classes of structures have the property EHD. In contrast,
we introduce Ehrenfeucht-Fraisse-games for (weak
with the bounding quantifier) and use them to show that the
infinite (order) tree does not have property EHD. As a consequence, a different
approach has to be taken in order to settle the question whether satisfiability
of (or even ) with constraints over the
infinite (order) tree is decidable
Bounded Synthesis of Reactive Programs
Most algorithms for the synthesis of reactive systems focus on the
construction of finite-state machines rather than actual programs. This often
leads to badly structured, unreadable code. In this paper, we present a bounded
synthesis approach that automatically constructs, from a given specification in
linear-time temporal logic (LTL), a program in Madhusudan's simple imperative
language for reactive programs. We develop and compare two principal approaches
for the reduction of the synthesis problem to a Boolean constraint satisfaction
problem. The first reduction is based on a generalization of bounded synthesis
to two-way alternating automata, the second reduction is based on a direct
encoding of the program syntax in the constraint system. We report on
preliminary experience with a prototype implementation, which indicates that
the direct encoding outperforms the automata approach
Symmetric Strategy Improvement
Symmetry is inherent in the definition of most of the two-player zero-sum
games, including parity, mean-payoff, and discounted-payoff games. It is
therefore quite surprising that no symmetric analysis techniques for these
games exist. We develop a novel symmetric strategy improvement algorithm where,
in each iteration, the strategies of both players are improved simultaneously.
We show that symmetric strategy improvement defies Friedmann's traps, which
shook the belief in the potential of classic strategy improvement to be
polynomial
SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
Counterexamples Revisited: Principles, Algorithms, Applications
Abstract. Algorithmic counterexample generation is a central feature of model checking which sets the method apart from other approaches such as theorem proving. The practical value of counterexamples to the verification engineer is evident, and for many years, counterexam-ple generation algorithms have been employed in model checking sys-tems, even though they had not been subject to an adequate fundamen-tal investigation. Recent advances in model checking technology such as counterexample-guided abstraction refinement have put strong em-phasis on counterexamples, and have lead to renewed interest both in fundamental and pragmatic aspects of counterexample generation. In this paper, we survey several key contributions to the subject includ-ing symbolic algorithms, results about the graph-theoretic structure of counterexamples, and applications to automated abstraction as well as software verification. Irrefutability is not a virtue of a theory (as people often think) but a vice
Mightyl: A compositional translation from mitl to timed automata
Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to Büchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends
Vectorial Languages and Linear Temporal Logic
International audienceDetermining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently, especially when dealing with very large texts. Considering words as vectors and working on them using vectorial (parallel) operations allows to solve the problem faster than in linear time using sequential computations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends only on the language accepted by the automaton. We give precise characterizations of vectorial algorithms for star-free, solvable and regular languages in terms of the vectorial operations allowed. We also consider classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of linear-time temporal logic characterizing solvable and regular languages is PSPACE-complete
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