17,063 research outputs found
An Efficient Algorithm for Monitoring Practical TPTL Specifications
We provide a dynamic programming algorithm for the monitoring of a fragment
of Timed Propositional Temporal Logic (TPTL) specifications. This fragment of
TPTL, which is more expressive than Metric Temporal Logic, is characterized by
independent time variables which enable the elicitation of complex real-time
requirements. For this fragment, we provide an efficient polynomial time
algorithm for off-line monitoring of finite traces. Finally, we provide
experimental results on a prototype implementation of our tool in order to
demonstrate the feasibility of using our tool in practical applications
Reinforcement Learning With Temporal Logic Rewards
Reinforcement learning (RL) depends critically on the choice of reward
functions used to capture the de- sired behavior and constraints of a robot.
Usually, these are handcrafted by a expert designer and represent heuristics
for relatively simple tasks. Real world applications typically involve more
complex tasks with rich temporal and logical structure. In this paper we take
advantage of the expressive power of temporal logic (TL) to specify complex
rules the robot should follow, and incorporate domain knowledge into learning.
We propose Truncated Linear Temporal Logic (TLTL) as specifications language,
that is arguably well suited for the robotics applications, together with
quantitative semantics, i.e., robustness degree. We propose a RL approach to
learn tasks expressed as TLTL formulae that uses their associated robustness
degree as reward functions, instead of the manually crafted heuristics trying
to capture the same specifications. We show in simulated trials that learning
is faster and policies obtained using the proposed approach outperform the ones
learned using heuristic rewards in terms of the robustness degree, i.e., how
well the tasks are satisfied. Furthermore, we demonstrate the proposed RL
approach in a toast-placing task learned by a Baxter robot
Robotic Planning under Hierarchical Temporal Logic Specifications
Past research into robotic planning with temporal logic specifications,
notably Linear Temporal Logic (LTL), was largely based on singular formulas for
individual or groups of robots. But with increasing task complexity, LTL
formulas unavoidably grow lengthy, complicating interpretation and
specification generation, and straining the computational capacities of the
planners. In order to maximize the potential of LTL specifications, we
capitalized on the intrinsic structure of tasks and introduced a hierarchical
structure to LTL specifications. In contrast to the "flat" structure, our
hierarchical model has multiple levels of compositional specifications and
offers benefits such as greater syntactic brevity, improved interpretability,
and more efficient planning. To address tasks under this hierarchical temporal
logic structure, we formulated a decomposition-based method. Each specification
is first broken down into a range of temporally interrelated sub-tasks. We
further mine the temporal relations among the sub-tasks of different
specifications within the hierarchy. Subsequently, a Mixed Integer Linear
Program is utilized to generate a spatio-temporal plan for each robot. Our
hierarchical LTL specifications were experimentally applied to domains of
robotic navigation and manipulation. Results from extensive simulation studies
illustrated both the enhanced expressive potential of the hierarchical form and
the efficacy of the proposed method.Comment: 8 pages, 4 figure
Refinement Calculus of Reactive Systems
Refinement calculus is a powerful and expressive tool for reasoning about
sequential programs in a compositional manner. In this paper we present an
extension of refinement calculus for reactive systems. Refinement calculus is
based on monotonic predicate transformers, which transform sets of post-states
into sets of pre-states. To model reactive systems, we introduce monotonic
property transformers, which transform sets of output traces into sets of input
traces. We show how to model in this semantics refinement, sequential
composition, demonic choice, and other semantic operations on reactive systems.
We use primarily higher order logic to express our results, but we also show
how property transformers can be defined using other formalisms more amenable
to automation, such as linear temporal logic (suitable for specifications) and
symbolic transition systems (suitable for implementations). Finally, we show
how this framework generalizes previous work on relational interfaces so as to
be able to express systems with infinite behaviors and liveness properties
A Fixpoint Calculus for Local and Global Program Flows
We define a new fixpoint modal logic, the visibly pushdown μ-calculus (VP-μ), as an extension of the modal μ-calculus. The models of this logic are execution trees of structured programs where the procedure calls and returns are made visible. This new logic can express pushdown specifications on the model that its classical counterpart cannot, and is motivated by recent work on visibly pushdown languages [4]. We show that our logic naturally captures several interesting program specifications in program verification and dataflow analysis. This includes a variety of program specifications such as computing combinations of local and global program flows, pre/post conditions of procedures, security properties involving the context stack, and interprocedural dataflow analysis properties. The logic can capture flow-sensitive and inter-procedural analysis, and it has constructs that allow skipping procedure calls so that local flows in a procedure can also be tracked. The logic generalizes the semantics of the modal μ-calculus by considering summaries instead of nodes as first-class objects, with appropriate constructs for concatenating summaries, and naturally captures the way in which pushdown models are model-checked. The main result of the paper is that the model-checking problem for VP-μ is effectively solvable against pushdown models with no more effort than that required for weaker logics such as CTL. We also investigate the expressive power of the logic VP-μ: we show that it encompasses all properties expressed by a corresponding pushdown temporal logic on linear structures (caret [2]) as well as by the classical μ-calculus. This makes VP-μ the most expressive known program logic for which algorithmic software model checking is feasible. In fact, the decidability of most known program logics (μ-calculus, temporal logics LTL and CTL, caret, etc.) can be understood by their interpretation in the monadic second-order logic over trees. This is not true for the logic VP-μ, making it a new powerful tractable program logic
Robust Multi-Agent Coordination from CaTL+ Specifications
We consider the problem of controlling a heterogeneous multi-agent system
required to satisfy temporal logic requirements. Capability Temporal Logic
(CaTL) was recently proposed to formalize such specifications for deploying a
team of autonomous agents with different capabilities and cooperation
requirements. In this paper, we extend CaTL to a new logic CaTL+, which is more
expressive than CaTL and has semantics over a continuous workspace shared by
all agents. We define two novel robustness metrics for CaTL+: the traditional
robustness and the exponential robustness. The latter is sound, differentiable
almost everywhere and eliminates masking, which is one of the main limitations
of the traditional robustness metric. We formulate a control synthesis problem
to maximize CaTL+ robustness and propose a two-step optimization method to
solve this problem. Simulation results are included to illustrate the increased
expressivity of CaTL+ and the efficacy of the proposed control synthesis
approach.Comment: Submitted to ACC 202
Temporalized logics and automata for time granularity
Suitable extensions of the monadic second-order theory of k successors have
been proposed in the literature to capture the notion of time granularity. In
this paper, we provide the monadic second-order theories of downward unbounded
layered structures, which are infinitely refinable structures consisting of a
coarsest domain and an infinite number of finer and finer domains, and of
upward unbounded layered structures, which consist of a finest domain and an
infinite number of coarser and coarser domains, with expressively complete and
elementarily decidable temporal logic counterparts.
We obtain such a result in two steps. First, we define a new class of
combined automata, called temporalized automata, which can be proved to be the
automata-theoretic counterpart of temporalized logics, and show that relevant
properties, such as closure under Boolean operations, decidability, and
expressive equivalence with respect to temporal logics, transfer from component
automata to temporalized ones. Then, we exploit the correspondence between
temporalized logics and automata to reduce the task of finding the temporal
logic counterparts of the given theories of time granularity to the easier one
of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym:
TPLP Category: Paper for Special Issue (Verification and Computational Logic)
Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September
200
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
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