Linear Temporal Logic Research Articles

Pardinus: A Temporal Relational Model Finder

This article presents \(\mathsf {Pardinus}\), an extension of the popular \(\mathsf {Kodkod}\) relational model finder with linear temporal logic (including past operators), to simplify the analysis of dynamic systems. \(\mathsf {Pardinus}\) includes a SAT-based bounded-model checking engine and an SMV-based complete model checking engine, both allowing iteration through the different instances (or counter-examples) of a specification. It also supports a decomposed parallel analysis strategy that improves the efficiency of both analysis engines on commodity multi-core machines.

Unification and Finite Model Property for Linear Step-Like Temporal Multi-Agent Logic with the Universal Modality

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

Formula omitted] is equivalent to [formula omitted

The organization of temporal properties into a Temporal Hierarchy proposed by Manna and Pnueli is central in the study of the expressive power of fragments of Linear Temporal Logic with Past (LTL+P). A crucial role is played by the Reactivity class, which itself forms a hierarchy consisting of the classes Reactivity(1), Reactivity(2), and so on, and it is proved to be expressively equivalent to LTL+P. The logic of Generalized Reactivity(1) (GR(1) for short), introduced in the context of reactive synthesis, expands the Reactivity(1) class (abbreviated R(1)) with safety formulas and multiple fairness conditions.In this paper, we prove that GR(1) is expressively equivalent to R(1). We first define a simple normal form for GR(1) formulas, and then we prove the expressive equivalence between GR(1) (in such a normal form) and R(1). In addition, we show that all the involved translations require only a linear increase in size. Finally, we lift these results to the general case proving that GR(N) is equivalent to R(N), for all N≥1.

A learning-based synthesis approach of reward asynchronous probabilistic games against the linear temporal logic winning condition.

The traditional synthesis problem is usually solved by constructing a system that fulfills given specifications. The system is constantly interacting with the environment and is opposed to the environment. The problem can be further regarded as solving a two-player game (the system and its environment). Meanwhile, stochastic games are often used to model reactive processes. With the development of the intelligent industry, these theories are extensively used in robot patrolling, intelligent logistics, and intelligent transportation. However, it is still challenging to find a practically feasible synthesis algorithm and generate the optimal system according to the existing research. Thus, it is desirable to design an incentive mechanism to motivate the system to fulfill given specifications. This work studies the learning-based approach for strategy synthesis of reward asynchronous probabilistic games against linear temporal logic (LTL) specifications in a probabilistic environment. An asynchronous reward mechanism is proposed to motivate players to gain maximized rewards by their positions and choose actions. Based on this mechanism, the techniques of the learning theory can be applied to transform the synthesis problem into the problem of computing the expected rewards. Then, it is proven that the reinforcement learning algorithm provides the optimal strategies that maximize the expected cumulative reward of the satisfaction of an LTL specification asymptotically. Finally, our techniques are implemented, and their effectiveness is illustrated by two case studies of robot patrolling and autonomous driving.

Reduction of Register Pushdown Systems with Freshness Property to Pushdown Systems in LTL Model Checking

Pushdown systems (PDS) are known as an abstract model of recursive programs, and model checking methods for PDS have been studied. Register PDS (RPDS) are PDS augmented by registers to deal with data values from an infinite domain in a restricted way. A linear temporal logic (LTL) model checking method for RPDS with regular valuations has been proposed; however, the method requires the register automata (RA) used for representing a regular valuation to be backward-deterministic. This paper proposes another approach to the same problem, in which the model checking problem for RPDS is reduced to that problem for PDS by constructing a PDS bisimulation equivalent to a given RPDS. The construction in the proposed method is simpler than the previous model checking method and does not require RAs deterministic or backward-deterministic, and the bisimulation equivalence clearly guarantees the correctness of this reduction. On the other hand, the proposed method requires every RPDS (and RA) to have the freshness property, in which whenever the RPDS updates a register with a data value not stored in any register or the stack top, the value should be fresh. This paper also shows that this model checking problem with regular valuations defined by general RA is undecidable, and thus the freshness constraint is essential in the proposed method.

Lifelong reinforcement learning with temporal logic formulas and reward machines

Continuously learning new tasks using high-level ideas or knowledge is a key capability of humans. In this paper, we propose lifelong reinforcement learning with sequential linear temporal logic formulas and reward machines (LSRM), which enables an agent to leverage previously learned knowledge to accelerate the learning of logically specified tasks. For a more flexible specification of tasks, we first introduce sequential linear temporal logic (SLTL), which is a supplement to the existing linear temporal logic (LTL) formal language. We then utilize reward machines (RMs) to exploit structural reward functions for tasks encoded with high-level events, and propose an automatic extension of RMs and efficient knowledge transfer over tasks for continuous lifelong learning. Experimental results show that LSRM outperforms methods that learn the target tasks from scratch by taking advantage of the task decomposition using SLTL and the knowledge transfer over RMs during the lifelong learning process.

Perception-Based Temporal Logic Planning in Uncertain Semantic Maps

In this article, we address a multi-robot planning problem in environments with partially unknown semantics. The environment is assumed to have a known geometric structure (e.g., walls) and to be occupied by static labeled landmarks with uncertain positions and classes. This modeling approach gives rise to an uncertain semantic map generated by semantic simultaneous localization and mapping algorithms. Our goal is to design control policies for robots equipped with noisy perception systems so that they can accomplish collaborative tasks captured by global temporal logic specifications. To specify missions that account for environmental and perceptual uncertainty, we employ a fragment of linear temporal logic (LTL), called co-safe LTL, defined over perception-based atomic predicates modeling probabilistic satisfaction requirements. The perception-based LTL planning problem gives rise to an optimal control problem, solved by a novel sampling-based algorithm, that generates open-loop control policies that are updated online to adapt to a continuously learned semantic map. We provide extensive experiments to demonstrate the efficiency of the proposed planning architecture.

An automated framework for verifying or refuting trace properties of extended finite state machines

Model checkers and interactive proof assistants are both used in the assurance of critical systems. Where theorem proving involves the use of axioms and inference rules to mathematically prove defined properties, model checkers can be used to provide concrete counterexamples to refute them. Thus, the two techniques can be thought of as complementary, and it is helpful to use both in tandem to take advantage of their respective strengths. However, this requires us to translate our system model and our desired properties between the two tools which is a time-consuming and error prone process if done manually. The key contribution of this work is a set of automated tools to translate between the Isabelle/HOL proof assistant and the Symbolic Analysis Laboratory (SAL) model checker. We focus on systems specified as extended finite state machines (EFSMs) and on properties specified in linear temporal logic (LTL). We present our representations in the two tools and demonstrate the applicability of our system with respect to an academic example and two realistic case studies. This is a significant contribution to broadening the applicability of these formal approaches, since it allows two powerful verification tools to be easily used in tandem without the risk of human error.

Monitoring Constraints and Metaconstraints with Temporal Logics on Finite Traces

Runtime monitoring is a central operational decision support task in business process management. It helps process executors to check on-the-fly whether a running process instance satisfies business constraints of interest, providing an immediate feedback when deviations occur. We study runtime monitoring of properties expressed in ltl f , a variant of the classical ltl (Linear-time Temporal Logic) that is interpreted over finite traces, and in its extension ldl f , a powerful logic obtained by combining ltl f with regular expressions. We show that ldl f is able to declaratively express, in the logic itself, not only the constraints to be monitored, but also the de facto standard rv -LTL monitors. On the one hand, this enables us to directly employ the standard characterization of ldl f based on finite-state automata to monitor constraints in a fine-grained way. On the other hand, it provides the basis for declaratively expressing sophisticated metaconstraints that predicate on the monitoring state of other constraints, and to check them by relying on standard logical services instead of ad hoc algorithms. We then report on how this approach has been effectively implemented using Java to manipulate ldl f formulae and their corresponding monitors, and the RuM rule mining suite as underlying infrastructure.

From linear temporal logic and limit-deterministic Büchi automata to deterministic parity automata

Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper, we describe a single exponential translation from limit-deterministic Büchi automata (LDBA) to DPA and show that it can be concatenated with a recent efficient translations from LTL to LDBA to yield a double exponential, ‘Safraless’ LTL-to-DPA construction. We also report on an implementation and a comparison with other LTL-to-DPA translations on several sets of formulas from the literature.

TEMPORAL REPRESENTATION OF THE ESSENCES OF THE SUBJECT AREA FOR THE CONSTRUCTION OF EXPLANATIONS IN INTELLIGENT SYSTEMS

The subject of research in the article is is the processes of constructing explanations in intelligent systems using causal relationships. The aim is to develop a representation of the entities of the subject area, taking into account the temporal aspect in order to represent the binary relations in time between the properties of the same entity. The construction of temporal relations between the properties of entities makes it possible to determine the probabilistic causal relationships between the states of these entities and use these dependencies to form explanations for the implemented decision-making process in the intelligent system, taking into account possible alternatives. Tasks: structuring the objects of the subject area, taking into account their essential properties for the decision-making process, including temporal; definition of classes of essences of subject area; determination of equivalence classes of entities of the subject area taking into account changes in the properties of these entities over time; development of a temporal model of representation of essences of subject area for construction of explanations in intellectual systems on the basis of definition of dependences in time between properties of essences. The approaches used are: set-theoretic approach, which is used to describe the classes of entities and classes of equivalence of entities of the subject area; linear temporal logic, which provides a representation of the relationship between entities in the temporal aspect. The following results were obtained. The structuring of the objects of the subject area is performed taking into account their properties, which are used in the decision-making process in the intellectual system; defined classes of entities; the classes of equivalence of entities of the subject area are defined as a kind of class of entities with the same values of key attributes, which makes it possible to take into account changes in these values over time; a temporal model of representation of the essences of the subject area is developed, which takes into account their static, dynamic properties and properties of time. Conclusions. The scientific novelty of the results is as follows. An equivalence class for entities is distinguished, which contains entities with the same key static properties and different dynamic properties considering the time of their change, which allows to reflect changes in the state of the entity in the decision-making process in the intelligent system. The temporal model of representation of essences of subject area which contains classes of equivalence of essences, and also temporal communications between properties of elements of these classes is offered. The selection of classes of equivalence of entities makes it possible to present the decision-making process in the intellectual system in the form of a sequence of temporal connections between the properties of entities of the subject area, and to form on this basis casual relationships between states of entities.

Programmable Logic Controllers Past Linear Temporal Logic for Monitoring Applications in Industrial Control Systems

Programmable Logic Controllers Past Linear Temporal Logic for Monitoring Applications in Industrial Control Systems

Temporal Logic Guided Meta Q-Learning of Multiple Tasks

Reinforcement learning (RL) based approaches have enabled robots to perform various tasks. However, most existing RL algorithms focus on learning a particular task, without considering generalization to new tasks. To address this issue, by combining meta learning and reinforcement learning, we develop a meta Q-learning of multi-task (MQMT) framework where the robot effectively learns a meta model from a diverse set of training tasks and then generalizes the learned model to a new set of tasks that have never been encountered during training using only a small amount of additional data. Particularly, the multiple tasks are specified by co-safe linear temporal logic specification. As a semantics-preserving rewriting operation, LTL progression is exploited to decompose training tasks into learnable sub-goals, which not only enables simultaneous learning of multiple tasks, but also facilitates reward design by converting non-Markovian reward process to Markovian ones. Reward shaping is further incorporated into the reward design to relax the sparse reward issue. The simulation and experiment results demonstrate the effectiveness of the MQMT framework.

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.

ASP-Based Declarative Process Mining

We put forward Answer Set Programming (ASP) as a solution approach for three classical problems in Declarative Process Mining: Log Generation, Query Checking, and Conformance Checking. These problems correspond to different ways of analyzing business processes under execution, starting from sequences of recorded events, a.k.a. event logs. We tackle them in their data-aware variant, i.e., by considering events that carry a payload (set of attribute-value pairs), in addition to the performed activity, specifying processes declaratively with an extension of linear-time temporal logic over finite traces (LTLf). The data-aware setting is significantly more challenging than the control-flow one: Query Checking is still open, while the existing approaches for the other two problems do not scale well. The contributions of the work include an ASP encoding schema for the three problems, their solution, and experiments showing the feasibility of the approach.

Bridging LTLf Inference to GNN Inference for Learning LTLf Formulae

Learning linear temporal logic on finite traces (LTLf) formulae aims to learn a target formula that characterizes the high-level behavior of a system from observation traces in planning. Existing approaches to learning LTLf formulae, however, can hardly learn accurate LTLf formulae from noisy data. It is challenging to design an efficient search mechanism in the large search space in form of arbitrary LTLf formulae while alleviating the wrong search bias resulting from noisy data. In this paper, we tackle this problem by bridging LTLf inference to GNN inference. Our key theoretical contribution is showing that GNN inference can simulate LTLf inference to distinguish traces. Based on our theoretical result, we design a GNN-based approach, GLTLf, which combines GNN inference and parameter interpretation to seek the target formula in the large search space. Thanks to the non-deterministic learning process of GNNs, GLTLf is able to cope with noise. We evaluate GLTLf on various datasets with noise. Our experimental results confirm the effectiveness of GNN inference in learning LTLf formulae and show that GLTLf is superior to the state-of-the-art approaches.

Bounded model checking distributed temporal logic

Abstract The distributed temporal logic (DTL) is a logic for reasoning about temporal properties of distributed systems from the local point of view of the system’s agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. Different versions of DTL have been proposed over the years for a number of different applications, reflecting different perspectives on how non-local information can be accessed by each agent. In a recent paper, an automata-theoretic approach to model check DTL was proposed Subtil et al. (2020, Technical Report). Herein, we follow a different approach and adapt the bounded model-checking (BMC) algorithm for linear temporal logic to the case of DTL (see Biere et al. (2003, Adv. Comput., 58, 117–148) and Biere et al. (1999, TACAS 1999, 193–207)). For that purpose, a new notion of bounded semantics for DTL is proposed. In the BMC approach, the witness problem is translated to the satisfiability of a propositional formula that can be addressed (efficiently) by SAT solvers. An important application for this approach is verification of security protocols (Basin et al. (2011, Theoret. Comput. Sci., 412, 4007–4043); Caleiro et al. (2005, Electron. Notes Theor. Comput. Sci., 125, 67–89)).

Formal verification of persistence and liveness in the trust-based blockchain crowdsourcing consensus protocol

Crowdsourcing is a potential computing paradigm that exploits collective human intelligence to solve complex tasks, but it suffers from various safety and security problems. Blockchain has emerged as a promising technology to address most of the security issues, however, it is challenging to find an appropriate and trusted blockchain-based consensus protocol for crowdsourcing services. This work proposes a novel Trust-based Blockchain Crowdsourcing consensus protocol that selects a leader and validators based on various trust factors. The proposed protocol addresses a major issue of ensuring correctness associated with the safety and security-critical systems which has a vital importance because failure of such systems may lead to adverse consequences. Mainly it is focused on persistence and liveness properties preventing invalid block insertion and consensus delay attacks. Model checking technique is utilized because of its effectiveness and automatic nature to perform formal verification. The proposed protocol is specified using Communicating Sequential Programs, and the persistence and liveness properties are specified through Linear Temporal Logic. The model verification is performed by giving the formal model and the properties as input to the Process Analysis Toolkit which checks for the satisfaction or violation of the properties.

On the Expressive Power of Planning Formalisms in Conjunction with LTL

Linear Temporal Logic (LTL) has been widely employed in various planning formalisms, e.g., in the STRIPS formalism, in order to specify constraints over state trajectories in a planning problem. In this paper, we investigate the expressive power of two planning formalisms in conjunction with LTL that are most commonly seen in non-hierarchical planning and hierarchical planning respectively, namely the STRIPS formalism and the Hierarchical Task Network (HTN) formalism. We do so by interpreting the set of all solutions to a planning problem as a formal language and comparing it with other formal ones, e.g., star-free languages. Our results provide an in-depth insight into the theoretical properties of the investigated planning formalisms and henceforth explore the common structure shared by solutions to planning problems in certain planning formalisms.

LTL cross entropy optimisation for quadcopter task orchestration

ABSTRACT This paper presents a task orchestration framework for multi-agent systems utilising linear temporal logic (LTL) and cross entropy optimisation, a stochastic optimisation technique used for rare-event sampling. We define task orchestration as a combination of task decomposition, allocation and planning for a quadcopter or team of quadcopters given a high-level specification. Specifically, we consider tasks that are complex and consist of environment constraints, system constraints, or both, that must be satisfied. We first approach motion planning for the single agent case where transition systems for the environment allow tasks to be developed as linear temporal logic (LTL) specifications. Trajectories are then generated via motion primitives for a single quadcopter and optimised via cross entropy to ensure optimal satisfaction of a cost function. We extend this work to the multi-agent case where a team of homogeneous quadcopters are considered to satisfy an LTL specification. In order to provide faster computations and initial cost-agnostic sampling, we formulate the online version of multi-agent task allocation via cross entropy for tasks specified in LTL specifications. The results of this framework are verified in simulation and experimentally with a team of quadcopters.