Linear Temporal Logic Research Articles

Verifying chip designs at RTL level

As chip designs become increasingly complex, the potential for errors and defects in circuits inevitably rises, posing significant challenges to chip security and reliability. This study investigates the use of the SAT-based bounded model checking (BMC) for Propositional Projection Temporal Logic (PPTL) to verify Verilog chip designs at the register transfer level (RTL). To this end, we propose an algorithm to implement automated extraction of state transfer relations from AIGER netlist and construction of Kripke structure. Additionally, we employ PPTL with the full regular expressiveness to describe the circuit properties to be verified, especially the periodic repetitive properties. This is not possible with Linear Temporal Logic (LTL) and Computational Tree Logic (CTL). By combining the PPTL properties with finite system paths and transforming them into conjunctive normal forms (CNFs), we utilize an SAT solver for verification. Experimental results demonstrate that our verification tool, SAT-BMC4PPTL, achieves higher verification efficiency and comprehensiveness.

First order Büchi automata and their application to verification of LTL specifications

Büchi automata have applications in formal verification, e.g., in deciding whether a system satisfies given properties. We provide a definition of Büchi automata based on first order logics for representing infinite state systems, and investigate rules for proving emptiness and non-emptiness of such automata. We then apply these rules to solve the problem of verifying correctness of concurrent transition systems, leading to a relatively complete approach for proving and disproving LTL (Linear Temporal Logic) specifications. This approach overcomes weaknesses of existing work based on well-founded sets in the sense that the relative completeness does not depend on additional specification for ensuring progress of non-stuttering transitions. On the practical aspect, we provide a set of examples with an experimental verification condition generation tool to demonstrate the potential applicability of the approach for the verification of concurrent systems.

Fuzzy Linear Temporal Logic with Quality Constraints

As an extension of quantitative temporal logic, uncertain temporal logic essentially describes the temporal behavior of uncertain and incomplete systems, thus better solving search and decision-making problems in such systems. Fuzzy linear temporal logic (FLTL) is a focal point in uncertain temporal logic research. However, there are evident shortcomings in the current research outcomes. First, in previous FLTL studies, the practice of obtaining path reachability and formula satisfaction values independently and subsequently selecting the smaller of the two as the satisfaction value metric led to information loss. Furthermore, this simplistic information fusion approach fails to reflect the varying importance of these two types of information to the requirements. Second, computing path reachability and temporal logic formula satisfaction values separately may result in a mismatch between the two pieces of information with respect to the same path segment. Thus, the primary challenge lies in accurately integrating the satisfaction values of temporal logic formulas with the path reachability of the segments that yields these satisfaction values, utilizing various reasonable information synthesis methods, to ensure synchronization between path reachability and formula satisfaction values without incurring information loss. Additionally, it is crucial to reflect the different preference requirements for these two types of information. Moreover, the temporal logic formula characterizes system properties, with its sub-formulas delineating distinct sub-properties. Consequently, considering the varying importance preferences of sub-formulas is also significant. To address these deficiencies, we introduced quality constraint operators into FLTL, resulting in quality-constrained fuzzy linear temporal logic (QFLTL). This incorporation enables the synchronization and comprehensive fusion of path-reachability information and formula satisfaction values within the final semantic metric, thereby resolving the issues related to information synchronization and loss. Furthermore, it can accommodate the differing preference requirements between the two types of information and sub-properties during the information synthesis process. We defined the syntax and semantics of QFLTL and examined its expressive power and properties. Notably, we investigated the decidability of logical decision problems in QFLTL, encompassing validity, satisfiability, and model-checking issues. We proposed corresponding solution algorithms and analyzed their complexities.

Gödel–Dummett linear temporal logic

We investigate a version of linear temporal logic whose propositional fragment is Gödel–Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics: first a real-valued semantics, where statements have a degree of truth in the real unit interval, and second a ‘bi-relational’ semantics. We then show that these two semantics indeed define one and the same logic: the statements that are valid for the real-valued semantics are the same as those that are valid for the bi-relational semantics. This Gödel temporal logic does not have any form of the finite model property for these two semantics: there are non-valid statements that can only be falsified on an infinite model. However, by using the technical notion of a quasimodel, we show that every falsifiable statement is falsifiable on a finite quasimodel, yielding an algorithm for deciding if a statement is valid or not. Later, we strengthen this decidability result by giving an algorithm that uses only a polynomial amount of memory, proving that Gödel temporal logic is PSPACE-complete. We also provide a deductive calculus for Gödel temporal logic, and show this calculus to be sound and complete for the above-mentioned semantics, so that all (and only) the valid statements can be proved with this calculus.

Program Dependence Net and on-demand slicing for property verification of concurrent system and software

When checking concurrent software using a finite-state model, we face a formidable state explosion problem. One solution to this problem is dependence-based program slicing, whose use can effectively reduce verification time. It is orthogonal to other model-checking reduction techniques. However, when slicing concurrent programs for model checking, there are conversions between multiple irreplaceable models, and dependencies need to be found for variables irrelevant to the verified property, which results in redundant computation. To resolve this issue, we propose a Program Dependence Net (PDNet) based on Petri net theory. It is a unified model that combines a control-flow structure with dependencies to avoid conversions. For reduction, we present a PDNet slicing method to capture the relevant variables’ dependencies when needed. PDNet and its on-demand slicing in verifying linear temporal logic are used to significantly reduce computation cost. We implement a model-checking tool based on PDNet and its on-demand slicing and validate the advantages of our proposed methods.

SPIN-Based Linear Temporal Logic Path Planning for Ground Vehicle Missions with Motion Constraints on Digital Elevation Models.

Linear temporal logic (LTL) formalism can ensure the correctness of mobile robot planning through concise, readable, and verifiable mission specifications. For uneven terrain, planning must consider motion constraints related to asymmetric slope traversability and maneuverability. However, even though model checker tools like the open-source Simple Promela Interpreter (SPIN) include search optimization techniques to address the state explosion problem, defining a global LTL property that encompasses both mission specifications and motion constraints on digital elevation models (DEMs) can lead to complex models and high computation times. In this article, we propose a system model that incorporates a set of uncrewed ground vehicle (UGV) motion constraints, allowing these constraints to be omitted from LTL model checking. This model is used in the LTL synthesizer for path planning, where an LTL property describes only the mission specification. Furthermore, we present a specific parameterization for path planning synthesis using a SPIN. We also offer two SPIN-efficient general LTL formulas for representative UGV missions to reach a DEM partition set, with a specified or unspecified order, respectively. Validation experiments performed on synthetic and real-world DEMs demonstrate the feasibility of the framework for complex mission specifications on DEMs, achieving a significant reduction in computation cost compared to a baseline approach that includes a global LTL property, even when applying appropriate search optimization techniques on both path planners.

Task-Driven Reinforcement Learning With Action Primitives for Long-Horizon Manipulation Skills.

It is an interesting open problem to enable robots to efficiently and effectively learn long-horizon manipulation skills. Motivated to augment robot learning via more effective exploration, this work develops task-driven reinforcement learning with action primitives (TRAPs), a new manipulation skill learning framework that augments standard reinforcement learning algorithms with formal methods and parameterized action space (PAS). In particular, TRAPs uses linear temporal logic (LTL) to specify complex manipulation skills. LTL progression, a semantics-preserving rewriting operation, is then used to decompose the training task at an abstract level, informs the robot about their current task progress, and guides them via reward functions. The PAS, a predefined library of heterogeneous action primitives, further improves the efficiency of robot exploration. We highlight that TRAPs augments the learning of manipulation skills in both learning efficiency and effectiveness (i.e., task constraints). Extensive empirical studies demonstrate that TRAPs outperforms most existing methods.

A Petri nets-based modeling method for multi robot path planning

The construction of lunar bases is one of the core enabling technologies in current lunar exploration and development plans of various countries. However, to eliminate the constraints of high transportation costs and limited manned space technology, a new research plan is to employ multi robot teams to build lunar bases. The key to this solution is how to achieve path planning for complex tasks for multiple robots. Therefore, this article takes the exploration and collection area, lunar soil collection, and lunar soil transportation in the lunar base construction scene as complex task inputs, and studies a multi robot path planning modeling method based on Petri net model. Firstly, a Petri net model for multi robot motion was constructed. Meanwhile, linear temporal logic(LTL) language was used to describe the related tasks of lunar base construction. Finally, simulation validation was conducted in Matlab software and compared with the modeling method using switching systems. The results show that the total modeling time required for using the Petri net model is reduced by two orders of magnitude compared to the modeling time for a single task switching system model, indicating that the established Petri net multi robot model has advantages such as avoiding dimension explosion and computational efficiency.

Towards the exact complexity of realizability for Safety LTL

We study the realizability and strong satisfiability problems for SafetyLTL, a syntactic fragment of Linear Temporal Logic (▪) capturing safe formulas. While it is well-known that realizability for this fragment lies in ▪, the best-known lower bound is ▪-hardness. Surprisingly, closing this gap has proven an elusive task. Previous works have claimed first ▪-completeness [1] and later ▪-completeness [2] for this problem, but both of these proofs turned out to be incorrect.We revisit the problem of the exact classification of the complexity of realizability for ▪ through the lens of seemingly weaker fragments. While we cannot settle the question for ▪, we study a subfragment of it consisting of formulas of the form ▪, where α is a present formula over system variables and ψ contains Next as the only temporal operator. We prove that the realizability problem for this new fragment, which we call ▪, is ▪-complete, and observe that this fragment is equirealizable to existing more expressive fragments, such as the class ▪[3].Furthermore, we revisit the techniques used in the purported proof of ▪-completeness of Arteche and Hermo [1], and observe that, while incorrect in their original claims, their proofs can be modified to classify the complexity of strong satisfiability, a necessary condition for realizability introduced by Kupferman, Sadigh, and Seshia [4]. We prove that, with regards to strong satisfiability, the fragments ▪ and ▪ are in fact equivalent under polynomial-time many-one reductions.

Long-term path planning with optimal deployment of a charging station for monitoring photovoltaic solar farms

Quadrotor technology has become increasingly important in the field of photovoltaic (PV) solar farm monitoring, but short battery life is one of the primary factors limiting its further application. To address above issue, this study proposes a linear temporal logic (LTL)-based path planning algorithm that considers the need for charging together with multiple visits to PV equipments, a single visit to communication equipment, and the avoidance of restricted regions, which enables the long-term monitoring of PV solar farms. Particularly, the location of a charging station can be determined optimally and efficiently by a heuristic algorithm based on the nonlinear programming and branch and bound (NLP-BB) algorithm. The simulation results indicate that the proposed method effectively solves the long-term monitoring path planning problem that is coupled with the optimal deployment of the charging station.

ASQ-IT: Interactive explanations for reinforcement-learning agents

As reinforcement learning methods increasingly amass accomplishments, the need for comprehending their solutions becomes more crucial. Most explainable reinforcement learning (XRL) methods generate a static explanation depicting their developers' intuition of what should be explained and how. In contrast, literature from the social sciences proposes that meaningful explanations are structured as a dialog between the explainer and the explainee, suggesting a more active role for the user and her communication with the agent. In this paper, we present ASQ-IT – an interactive explanation system that presents video clips of the agent acting in its environment based on queries given by the user that describe temporal properties of behaviors of interest. Our approach is based on formal methods: queries in ASQ-IT's user interface map to a fragment of Linear Temporal Logic over finite traces (LTLf), which we developed, and our algorithm for query processing is based on automata theory. User studies show that end-users can understand and formulate queries in ASQ-IT and that using ASQ-IT assists users in identifying faulty agent behaviors.

Using experience classification for training non-Markovian tasks

Unlike standard Reinforcement Learning (RL) model, many real-world tasks are non-Markovian, which requires long-term memory and dependency. Hence solving a non-Markovian task is more difficult and challenging than solving a Markovian one. In this paper, we propose a novel RL approach for training non-Markovian tasks expressed in temporal logic LTLf (Linear Temporal Logic over Finite Traces). To this end, an encoding of linear complexity from LTLf into MDPs (Markov Decision Processes) is introduced in order to take advantage of advanced RL algorithms. We further propose an experience classification method based on the automaton structure (theoretically equivalent to LTLf specifications). An automatic reward shaping technique and a prioritized experience replay mechanism are developed to cooperate with the classification method to improve the performance of RL algorithms. We provide empirical evaluations on two widely used benchmark problems, Waterworld and Cartpole, both augmented with complex non-Markovian tasks. The evaluations are conducted with respect to the metrics of training speed, policy quality, convergence rates, computational efficiency and scalability etc. The experimental results show that our approach achieves superior performance over other relevant studies, specially with an average improvement of 133% in convergence rate and a reduction of 11% in training time.

Runtime verification on abstract finite state models

Finite-state models are ubiquitous in the study of concurrent systems, especially controllers and servers that operate in a repetitive cycle. In this paper, we show how to extract finite state models from a run of a multi-threaded Java program and carry out runtime verification of correctness properties. These properties include data-oriented and control-oriented properties; the former express correctness conditions over the data fields of objects, while the latter are concerned with the correct flow of control among the modules of larger software. As the extracted models can become very large for long runs, the focus of this paper is on constructing reduced models with user-defined abstraction functions that map a larger domain space to a smaller one. The abstraction functions should be chosen so that the resulting model is property preserving, i.e., proving a property on the abstract model carries over to the concrete model. The main contribution of this paper is in showing how runtime verification can be made efficient through online property checking on property-preserving abstract models. The property specification language resembles a propositional linear temporal logic augmented with simple datatypes and operators. Classic concurrency examples and larger case studies (Multi-rotor Drone Controller, OAuth Protocol) are presented in order to demonstrate the usefulness of our proposed techniques, which are incorporated in an Eclipse plug-in for runtime visualization and verification of Java programs.

VALIO: Visual attention-based linear temporal logic method for explainable out-of-the-loop identification

The phenomenon of being Out-Of-The-Loop (OOTL) can significantly undermine pilots’ performance and pose a threat to aviation safety. Previous attempts to identify OOTL status have primarily utilized “black-box” machine learning techniques, which fail to provide explainable insights into their findings. To address this gap, our study introduces a novel application of Linear Temporal Logic (LTL) methods within a framework named Visual Attention LTLf for Identifying OOTL (VALIO), leveraging eye-tracking technology to non-intrusively capture the pilots’ attentional focus. By encoding Areas of Interest (AOIs) and gaze durations within the cockpit into Visual Attention Traces (VAT), the method captures the spatial and temporal dimensions of visual attention. It enables the LTL methods to generate interpretable formulas that classify pilot behaviors and provide insights into the understanding of the OOTL phenomenon. Through a case study of a simulated flight experiment, we compared the efficacy of this approach using different time windows from 10 s to 75 s. The results demonstrate that VALIO’s performance is stable across all time windows with the best F1 score of 0.815 and the lowest F1 of 0.769. And it significantly outperforms the other machine learning methods when using time windows shorter than 30 s, signifying its ability to detect the OOTL status more in-timely. Moreover, the VALIO elucidates pilot behaviors through the derivation of human-readable LTLf formulas, offering the explainability of the results and insights into OOTL characteristics. Overall, this research proposes the VALIO framework as an improvement for OOTL identification in both performance and explainability.

Computing Unsatisfiable Cores for LTLf Specifications

Linear-time temporal logic on finite traces (LTLf) is rapidly becoming a de-facto standard to produce specifications in many application domains (including planning, business process management, run-time monitoring, and reactive synthesis). Several studies have challenged the satisfiability problem thus far. In this paper, we focus instead on unsatisfiable LTLf specifications, with the objective of extracting the subset of formulae that cause inconsistencies within them, i.e., the unsatisfiable cores. We provide four algorithms to this end, which leverage the adaptation of a range of state-of-the-art algorithms to LTLf satisfiability checking. We implement those algorithms extending the respective implementations and carry out an experimental evaluation on a set of reference benchmarks, restricting to the unsatisfiable specifications. The results put in evidence that the different algorithms and tools exhibit complementary features determining their efficiency and efficacy. Indeed, our findings suggest exploring different strategies and algorithmic solutions for the extraction of unsatisfiable cores from LTLf specifications, thus confirming the challenging and multi-faceted nature of this problem.

Reaction mining for reaction systems

Reaction systems are a formal model for computational processing in which reactions operate on sets of entities (molecules) providing a framework for dealing with qualitative aspects of biochemical systems. This paper is concerned with reaction systems in which entities can have discrete concentrations, and so reactions operate on multisets rather than sets of entities. The resulting framework allows one to deal with quantitative aspects of reaction systems, and a bespoke linear-time temporal logic allows one to express and verify a wide range of key behavioural system properties. In practical applications, a reaction system with discrete concentrations may only be partially specified, and the possibility of an effective automated calculation of the missing details provides an attractive design approach. With this idea in mind, the current paper discusses parametric reaction systems with parameters representing unknown parts of hypothetical reactions. The main result is a method aimed at replacing the parameters in such a way that the resulting reaction system operating in a specified external environment satisfies a given temporal logic formula.This paper provides an encoding of parametric reaction systems in smt, and outlines a synthesis procedure based on bounded model checking for solving the synthesis problem. It also reports on the initial experimental results demonstrating the feasibility of the novel synthesis method.

DECLAREd: A Polytime LTLf Fragment

This paper considers a specification rewriting meachanism for a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, working through an equational logic and rewriting mechanism under customary practitioner assumptions from the Business Process Management literature. By rewriting the specification into an equivalent formula which might be easier to compute, we aim to streamline current state-of-the-art temporal artificial intelligence algorithms working on temporal logic. As this specification rewriting mechanism is ultimately also able to determine with the provided specification is a tautology (always true formula) or a formula containing a temporal contradiction, by detecting the necessity of a specific activity label to be both present and absent within a log, this implies that the proved mechanism is ultimately a SAT-solver for DECLAREd. We prove for the first time, to the best of our knowledge, that this fragment is a polytime fragment of LTLf, while all the previously-investigated fragments or extensions of such a language were in polyspace. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) algorithms, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times, thus motivating the pressing need of this approach for practical temporal artificial intelligence scenarios. We validate such claims by testing such algorithms over a Cybersecurity dataset.

A Framework for Simultaneous Task Allocation and Planning under Uncertainty

We present novel techniques for simultaneous task allocation and planning in multi-robot systems operating under uncertainty. By performing task allocation and planning simultaneously, allocations are informed by individual robot behaviour, creating more efficient team behaviour. We go beyond existing work by planning for task reallocation across the team given a model of partial task satisfaction under potential robot failures and uncertain action outcomes. We model the problem using Markov decision processes, with tasks encoded in co-safe linear temporal logic, and optimise for the expected number of tasks completed by the team. To avoid the inherent complexity of joint models, we propose an alternative model that simultaneously considers task allocation and planning, but in a sequential fashion. We then build a joint policy from the sequential policy obtained from our model, thus allowing for concurrent policy execution. Furthermore, to enable adaptation in the case of robot failures, we consider replanning from failure states and propose an approach to preemptively replan in an anytime fashion, replanning for more probable failure states first. Our method also allows us to quantify the performance of the team by providing an analysis of properties such as the expected number of completed tasks under concurrent policy execution. We implement and extensively evaluate our approach on a range of scenarios. We compare its performance to a state-of-the-art baseline in decoupled task allocation and planning: sequential single-item auctions. Our approach outperforms the baseline in terms of computation time and the number of times replanning is required on robot failure.

Singly exponential translation of alternating weak Büchi automata to unambiguous Büchi automata

We introduce a method for translating an alternating weak Büchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous Büchi automaton (UBA). Our translations generalize constructions for Linear Temporal Logic (LTL), a less expressive specification language than LDL. In classical constructions, LTL formulas are first translated to alternating very weak Büchi automata (AVAs)—automata that have only singleton strongly connected components (SCCs); these AVAs are then handled by efficient disambiguation procedures. However, general AWAs can have larger SCCs, which complicates disambiguation. Currently, the only available disambiguation procedure has to go through an intermediate construction of nondeterministic Büchi automata (NBAs), which would incur an exponential blow-up of its own. We introduce a translation from general AWAs to UBAs with a singly exponential blow-up, which also immediately provides a singly exponential translation from LDL to UBAs. Interestingly, the complexity of our translation is smaller than the best known disambiguation algorithm for NBAs (broadly (0.53n)n vs. (0.76n)n), while the input of our construction can be exponentially more succinct.

Deep Learning-Enhanced Sampling-Based Path Planning for LTL Mission Specifications.

The presented paper introduces a novel path planning algorithm designed for generating low-cost trajectories that fulfill mission requirements expressed in Linear Temporal Logic (LTL). The proposed algorithm is particularly effective in environments where cost functions encompass the entire configuration space. A core contribution of this paper is the presentation of a refined approach to sampling-based path planning algorithms that aligns with the specified mission objectives. This enhancement is achieved through a multi-layered framework approach, enabling a simplified discrete abstraction without relying on mesh decomposition. This abstraction is especially beneficial in complex or high-dimensional environments where mesh decomposition is challenging. The discrete abstraction effectively guides the sampling process, influencing the selection of vertices for extension and target points for steering in each iteration. To further improve efficiency, the algorithm incorporates a deep learning-based extension, utilizing training data to accurately model the optimal trajectory distribution between two points. The effectiveness of the proposed method is demonstrated through simulated tests, which highlight its ability to identify low-cost trajectories that meet specific mission criteria. Comparative analyses also confirm the superiority of the proposed method compared to existing methods.