An official website of the United States government
Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is Linear Temporal Logic (LTL). Policy synthesis on MDPs for properties specified in LTL has been well studied. LTL, however, is defined over infinite traces, while many properties of interest are inherently finite. Linear Temporal Logic over finite traces (LTLf ) has been used to express such properties, but no tools exist to solve policy synthesis for MDP behaviors given finite-trace properties. We present two algorithms for solving this synthesis problem: the first via reduction of LTLf to LTL and the second using native tools for LTLf . We compare the scalability of these two approaches for synthesis and show that the native approach offers better scalability compared to existing automaton generation tools for LTL.
more »
« less
Synthesizing Good-Enough Strategies for LTLf Specifications
We consider the problem of synthesizing good-enough (GE)-strategies for linear temporal logic (LTL) over finite traces or LTLf for short.The problem of synthesizing GE-strategies for an LTL formula φ over infinite traces reduces to the problem of synthesizing winning strategies for the formula (∃Oφ)⇒φ where O is the set of propositions controlled by the system.We first prove that this reduction does not work for LTLf formulas.Then we show how to synthesize GE-strategies for LTLf formulas via the Good-Enough (GE)-synthesis of LTL formulas.Unfortunately, this requires to construct deterministic parity automata on infinite words, which is computationally expensive.We then show how to synthesize GE-strategies for LTLf formulas by a reduction to solving games played on deterministic Büchi automata, based on an easier construction of deterministic automata on finite words.We show empirically that our specialized synthesis algorithm for GE-strategies outperforms the algorithms going through GE-synthesis of LTL formulas by orders of magnitude.
more »
« less
- Award ID(s):
- 1830549
- PAR ID:
- 10376723
- Date Published:
- Journal Name:
- IJCAI
- Page Range / eLocation ID:
- 4144 to 4151
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Linear Temporal Logic (LTL) synthesis aims at automatically synthesizing a program that complies with desired properties expressed in LTL. Unfortunately it has been proved to be too difficult computationally to perform full LTL synthesis. There have been two success stories with LTL synthesis, both having to do with the form of the specification. The first is the GR(1) approach: use safety conditions to determine the possible transitions in a game between the environment and the agent, plus one powerful notion of fairness, Generalized Reactivity(1), or GR(1). The second, inspired by AI planning, is focusing on finite-trace temporal synthesis, with LTLf (LTL on finite traces) as the specification language. In this paper we take these two lines of work and bring them together. We first study the case in which we have an LTLf agent goal and a GR(1) assumption. We then add to the framework safety conditions for both the environment and the agent, obtaining a highly expressive yet still scalable form of LTL synthesis.more » « less
-
Abate, Alessandro; Cannon, Mark; Margellos, Kostas; Papachristodoulou, Antonis (Ed.)In this paper, we introduce a data-driven framework for synthesis of provably-correct controllers for general nonlinear switched systems under complex specifications. The focus is on systems with unknown disturbances whose effects on the dynamics of the system is nonlinear. The specification is assumed to be given as linear temporal logic over finite traces (LTLf) formulas. Starting from observations of either the disturbance or the state of the system, we first learn an ambiguity set that contains the unknown distribution of the disturbances with a user-defined confidence. Next, we obtain a robust Markov decision process (RMDP) as a finite abstraction of the system. By composing the RMDP with the automaton obtained from the LTLf formula and performing optimal robust value iteration on the composed RMDP, we synthesize a strategy that yields a high probability that the uncertain system satisfies the specifications. Our empirical evaluations on systems with a wide variety of disturbances show that the strategies synthesized with our approach lead to high satisfaction probabilities and validate the theoretical guarantees.more » « less
-
Runtime verificationis a lightweight method for monitoring the formal specification of a system during its execution. It has recently been shown that a given state predicate can be monitored consistently by a set of crash-prone asynchronousdistributedmonitors observing the system, only if each monitor can emit verdicts taken from alarge enoughfinite set. We revisit this impossibility result in the concrete context of linear-time logic (ltl) semantics for runtime verification, that is, when the correctness of the system is specified by anltlformula on its execution traces. First, we show that monitors synthesized based on the 4-valued semantics ofltl(rv-ltl) may result in inconsistent distributed monitoring, even for some simpleltlformulas. More generally, given anyltlformula φ, we relate the number of different verdicts required by the monitors for consistently monitoring φ, with a specific structural characteristic of φ called itsalternation number. Specifically, we show that, for everyk ≥ 0, there is anltlformula φ with alternation number kthat cannot be verified at runtime by distributed monitors emitting verdicts from a set of cardinality smaller thank+ 1. On the positive side, we define a family of logics, calleddistributedltl(abbreviated asdltl), parameterized byk≥ 0, which refinesrv-ltlby incorporating2k+ 4 truth values. Our main contribution is to show that, for everyk≥ 0, everyltlformula φ with alternation number kcan be consistently monitored by distributed monitors, each running an automaton based on a (2 ⌈k/2 ⌉ +4)-valued logic taken from thedltlfamily.more » « less
-
null (Ed.)We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.24963/ijcai.2021/570
