119,231 research outputs found
Linear temporal logic for regular cost functions
Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is that exact values are not considered, but only estimated.
In this paper, we define an extension of Linear Temporal Logic (LTL) over finite words to describe cost functions. We give an explicit translation from this new logic to automata. We then algebraically characterize the expressive power of this logic, using a new syntactic congruence for cost functions introduced in this paper
Parametric Linear Dynamic Logic
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL)
that is able to express all -regular specifications while still
maintaining many of LTL's desirable properties like an intuitive syntax and a
translation into non-deterministic B\"uchi automata of exponential size. But
LDL lacks capabilities to express timing constraints. By adding parameterized
operators to LDL, we obtain a logic that is able to express all
-regular properties and that subsumes parameterized extensions of LTL
like Parametric LTL and PROMPT-LTL. Our main technical contribution is a
translation of PLDL formulas into non-deterministic B\"uchi word automata of
exponential size via alternating automata. This yields a PSPACE model checking
algorithm and a realizability algorithm with doubly-exponential running time.
Furthermore, we give tight upper and lower bounds on optimal parameter values
for both problems. These results show that PLDL model checking and
realizability are not harder than LTL model checking and realizability.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Reasoning about Actions with Temporal Answer Sets
In this paper we combine Answer Set Programming (ASP) with Dynamic Linear
Time Temporal Logic (DLTL) to define a temporal logic programming language for
reasoning about complex actions and infinite computations. DLTL extends
propositional temporal logic of linear time with regular programs of
propositional dynamic logic, which are used for indexing temporal modalities.
The action language allows general DLTL formulas to be included in domain
descriptions to constrain the space of possible extensions. We introduce a
notion of Temporal Answer Set for domain descriptions, based on the usual
notion of Answer Set. Also, we provide a translation of domain descriptions
into standard ASP and we use Bounded Model Checking techniques for the
verification of DLTL constraints.Comment: To appear in Theory and Practice of Logic Programmin
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis
The classic approaches to synthesize a reactive system from a linear temporal
logic (LTL) specification first translate the given LTL formula to an
equivalent omega-automaton and then compute a winning strategy for the
corresponding omega-regular game. To this end, the obtained omega-automata have
to be (pseudo)-determinized where typically a variant of Safra's
determinization procedure is used. In this paper, we show that this
determinization step can be significantly improved for tool implementations by
replacing Safra's determinization by simpler determinization procedures. In
particular, we exploit (1) the temporal logic hierarchy that corresponds to the
well-known automata hierarchy consisting of safety, liveness, Buechi, and
co-Buechi automata as well as their boolean closures, (2) the non-confluence
property of omega-automata that result from certain translations of LTL
formulas, and (3) symbolic implementations of determinization procedures for
the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular,
we present convincing experimental results that demonstrate the practical
applicability of our new synthesis procedure
Metric Dynamic Equilibrium Logic
In temporal extensions of Answer Set Programming (ASP) based on linear-time,
the behavior of dynamic systems is captured by sequences of states. While this
representation reflects their relative order, it abstracts away the specific
times associated with each state. In many applications, however, timing
constraints are important like, for instance, when planning and scheduling go
hand in hand. We address this by developing a metric extension of linear-time
Dynamic Equilibrium Logic, in which dynamic operators are constrained by
intervals over integers. The resulting Metric Dynamic Equilibrium Logic
provides the foundation of an ASP-based approach for specifying qualitative and
quantitative dynamic constraints. As such, it constitutes the most general
among a whole spectrum of temporal extensions of Equilibrium Logic. In detail,
we show that it encompasses Temporal, Dynamic, Metric, and regular Equilibrium
Logic, as well as its classic counterparts once the law of the excluded middle
is added.Comment: arXiv admin note: text overlap with arXiv:2304.1477
A PAC Learning Algorithm for LTL and Omega-regular Objectives in MDPs
Linear temporal logic (LTL) and omega-regular objectives -- a superset of LTL
-- have seen recent use as a way to express non-Markovian objectives in
reinforcement learning. We introduce a model-based probably approximately
correct (PAC) learning algorithm for omega-regular objectives in Markov
decision processes. Unlike prior approaches, our algorithm learns from sampled
trajectories of the system and does not require prior knowledge of the system's
topology
Mungojerrie:Linear-Time Objectives in Model-Free Reinforcement Learning
Mungojerrie is an extensible tool that provides a framework to translate linear-time objectives into reward for reinforcement learning (RL). The tool provides convergent RL algorithms for stochastic games, reference implementations of existing reward translations for ω -regular objectives, and an internal probabilistic model checker for ω -regular objectives. This functionality is modular and operates on shared data structures, which enables fast development of new translation techniques. Mungojerrie supports finite models specified in PRISM and ω -automata specified in the HOA format, with an integrated command line interface to external linear temporal logic translators. Mungojerrie is distributed with a set of benchmarks for ω -regular objectives in RL.</p
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