Product Of Automata Research Articles

Real-time reactive task allocation and planning of large heterogeneous multi-robot systems with temporal logic specifications

Existing methods for the task allocation and planning (TAP) of multi-robot systems with temporal logic specifications mainly rely on optimization-based approaches or graph search techniques applied to the product automaton. However, these methods suffer from high computational cost and scale poorly with the number of robots and the complexity of temporal logic tasks, thus limiting the applicability in real-time implementation, especially for large multi-robot systems. To address these challenges, this work develops a novel TAP framework that can solve reactive temporal logic planning problems for large-scale heterogeneous multi-robot systems (HMRS) in real time. Specifically, we develop a planning decision tree (PDT) to represent the task progression and task allocation specialized for HMRS with temporal logic specifications. Based on the PDT, we develop two key search algorithms—the planning decision tree search (PDTS) and the interactive planning decision tree search (IPDTS)—where PDTS generates an offline plan which will be modified online by PDTS and IPDTS jointly to enable fast reactive planning if environmental changes or temporary tasks occur. Such a design can generate satisfying plan for HMRS with multiple orders of magnitude more robots than those that existing methods can manipulate. Rigorous analysis shows that the PDT-based planning is feasible (i.e., the generated plan is applicable) and complete (i.e., a feasible plan, if exits, is guaranteed to be found). The algorithm complexity further indicates that the solution time is only linearly proportional to the robot numbers and types. Simulation and experiment results demonstrate that reactive plan can be generated for large HMRS in real-time, which outperforms the state-of-the-art methods.

A Novel Approach to Construct Finite Automata Using Grid and Product Automata

This research aims to utilize an organized grid-based strategy to make the development of complex Finite Automata easier. Product Automata are used to merge many automata into a single automaton to integrate various computing processes. Combining these methodologies provides novel methods of improving the scalability and efficiency of automata building, broadening the field of research for automata theory and its applications. The scalability of this developed automated system will benefit sectors such as automotive production and logistics. The results indicate considerable improvements in construction time, memory usage, scalability, and resilience compared to older approaches. The performance of the developed method, as measured by construction time, memory utilization, scalability, robustness, application range, and complexity, is 25% to 50% higher than that of traditional methodologies in the literature.

A Constraint Solving Approach to Parikh Images of Regular Languages

A common problem in string constraint solvers is computing the Parikh image, a linear arithmetic formula that describes all possible combinations of character counts in strings of a given language. Automata-based string solvers frequently need to compute the Parikh image of products (or intersections) of finite-state automata, in particular when solving string constraints that also include the integer data-type due to operations like string length and indexing. In this context, the computation of Parikh images often turns out to be both prohibitively slow and memory-intensive. This paper contributes a new understanding of how the reasoning about Parikh images can be cast as a constraint solving problem, and questions about Parikh images be answered without explicitly computing the product automaton or the exact Parikh image. The paper shows how this formulation can be efficiently implemented as a calculus, PC*, embedded in an automated theorem prover supporting Presburger logic. The resulting standalone tool Catra is evaluate on constraints produced by the Ostrich+ string solver when solving standard string constraint benchmarks involving integer operations. The experiments show that PC* strictly outperforms the standard approach by Verma et al. to extract Parikh images from finite-state automata, as well as the over-approximating method recently described by Janků and Turoňová by a wide margin, and for realistic timeouts (under 60 s) also the nuXmv model checker. When added as the Parikh image backend of Ostrich+ to the Ostrich string constraint solver’s portfolio, it boosts its results on the quantifier-free strings with linear integer algebra track of SMT-COMP 2023 (QF_SLIA) enough to solve the most Unsat instances in that track of all competitors.

Pangenome comparison via ED strings.

An elastic-degenerate (ED) string is a sequence of sets of strings. It can also be seen as a directed acyclic graph whose edges are labeled by strings. The notion of ED strings was introduced as a simple alternative to variation and sequence graphs for representing a pangenome, that is, a collection of genomic sequences to be analyzed jointly or to be used as a reference. In this study, we define notions of matching statistics of two ED strings as similarity measures between pangenomes and, consequently infer a corresponding distance measure. We then show that both measures can be computed efficiently, in both theory and practice, by employing the intersection graph of two ED strings. We also implemented our methods as a software tool for pangenome comparison and evaluated their efficiency and effectiveness using both synthetic and real datasets. As for efficiency, we compare the runtime of the intersection graph method against the classic product automaton construction showing that the intersection graph is faster by up to one order of magnitude. For showing effectiveness, we used real SARS-CoV-2 datasets and our matching statistics similarity measure to reproduce a well-established clade classification of SARS-CoV-2, thus demonstrating that the classification obtained by our method is in accordance with the existing one.

Finite-Memory Supervisory Control of Discrete Event Systems for LTL[$\mathcal {F}$] Specifications

In this article, we study a supervisory control problem under a constraint on memory size as well as a constraint described by a class of quantitative linear temporal logic, which enables us to consider how well the specification is satisfied. Our control objective is to design a finite-memory supervisor such that the satisfaction value of the specification formula on the controlled system is larger than or equal to a given threshold. We adopt a Safraless synthesis methodology and reduce the problem to solving a safety game parameterized with the memory size of a supervisor. On the safety game, we compute a winning strategy by leveraging a ranking function. Our definition of the ranking function relies on the product automaton, which captures both the behavior of the controlled plant and that of an automaton transformed from the specification and the threshold.

Temporal Logic Planning and Receding Horizon Control for Signal Source Localization

This article copes with signal source localization by employing a receding horizon control approach with temporal logic planning in the light of a single mobile robot. First, a temporal logic planning approach is proposed such that the task requirements from the temporal logic specifications can be effectively dealt with based on the product automaton in an offline fashion. Second, in order to label the key nodes of the product automaton, a particle filter is utilized to predict the source positions as the key nodes. Third, on the basis of the product automaton, a receding horizon control approach with temporal logic planning is developed to produce the robot’s trajectory that satisfies a given linear temporal logic specification. Finally, the effectiveness of the proposed control approach is illustrated for signal source localization.

Abstraction-based synthesis for stochastic systems with omega-regular objectives

This paper studies the synthesis of controllers for discrete-time, continuous state stochastic systems subject to omega-regular specifications using finite-state abstractions. Omega-regular properties allow specifying complex behaviors and encompass, for example, linear temporal logic. First, we present a synthesis algorithm for minimizing or maximizing the probability that a discrete-time switched stochastic system with a finite number of modes satisfies an omega-regular property. Our approach relies on a finite-state abstraction of the underlying dynamics in the form of a Bounded-parameter Markov Decision Process arising from a finite partition of the system’s domain. Such Markovian abstractions allow for a range of probabilities of transition between states for each selected action representing a mode of the original system. Our method is built upon an analysis of the Cartesian product between the abstraction and a Deterministic Rabin Automaton encoding the specification of interest or its complement. Specifically, we show that synthesis can be decomposed into a qualitative problem, where the so-called greatest permanent winning components of the product automaton are created, and a quantitative problem, which requires maximizing the probability of reaching this component in the worst-case instantiation of the transition intervals. Additionally, we propose a quantitative metric for measuring the quality of the designed controller with respect to the continuous abstracted states and devise a specification-guided domain partition refinement heuristic with the objective of reaching a user-defined optimality target. Next, we present a method for computing control policies for stochastic systems with a continuous set of available inputs. In this case, the system is assumed to be affine in input and disturbance, and we derive a technique for solving the qualitative and quantitative problems in the resulting finite-state abstractions of such systems. For this, we introduce a new type of abstractions called Controlled Interval-valued Markov Chains. Specifically, we show that the greatest permanent winning component of such abstractions are found by appropriately partitioning the continuous input space in order to generate a bounded-parameter Markov decision process that accounts for all possible qualitative transitions between the finite set of states. Then, the problem of maximizing the probability of reaching these components is cast as a (possibly non-convex) optimization problem over the continuous set of available inputs. A metric of quality for the synthesized controller and a partition refinement scheme are described for this framework as well. Finally, we present a detailed case study.

Designing a Safe Intersection Management Algorithm using Formal Methods

This paper presents an approach for designing correct-by-construction Autonomous Intersection Management (AIM) algorithms for autonomous vehicles using formal methods. The task of the AIM is to establish the right-of-way (priorities) for the incoming autonomous vehicles. Based on the assumption that the vehicles communicate their planned paths, namely the entering and the exiting points of the intersection, e.g., over V2I protocol, the AIM makes sure that the trajectories of the incoming vehicles do not overlap. We argue that traffic efficiency and flow can be increased with an intelligent algorithm; however, the safety of this algorithm should be verified formally and then tested in a simulation environment. In this paper, we use formal methods for synthesizing a control protocol with safety guarantees. The intersection and the incoming vehicles are modeled as transition systems; their composition constitutes the overall concurrent system. The control protocol is synthesized using a set of specifications (safety properties) written in Linear Temporal Logic (LTL). These LTL specifications are then converted to Büchi automata, and the product automaton with the concurrent system results in a new transition system verified by model-checking. Formal verification is complemented by simulation-based tests conducted in MOBATSim (Model-based Autonomous Traffic Simulation Framework). This approach increases the validation envelope for the correct behavior of the system and the validity of the assumptions made for modeling. The synthesis algorithms developed for MATLAB implementation are also published as an open-source library with documentation and case studies.

Online Motion Planning With Soft Metric Interval Temporal Logic in Unknown Dynamic Environment

Motion planning of an autonomous system with high-level specifications has wide applications. However, research of formal languages involving timed temporal logic is still under investigation. Furthermore, many existing results rely on a key assumption that user-specified tasks are feasible in the given environment. Challenges arise when the operating environment is dynamic and unknown since the environment can be found prohibitive, leading to potentially conflicting tasks where pre-specified timed missions cannot be fully satisfied. Such issues become even more challenging when considering time-bound requirements. To address these challenges, this work proposes a control framework that considers hard constraints to enforce safety requirements and soft constraints to enable task relaxation. The metric interval temporal logic (MITL) specifications are employed to deal with time-bound constraints. By constructing a relaxed timed product automaton, an online motion planning strategy is synthesized with a receding horizon controller to generate policies, achieving multiple objectives in decreasing order of priority 1) formally guarantee the satisfaction of hard safety constraints; 2) mostly fulfill soft timed tasks; and 3) collect time-varying rewards as much as possible. Another novelty of the relaxed structure is to consider violations of both time and tasks for infeasible cases. Simulation results are provided to validate the proposed approach.

An Abstraction-Free Method for Multirobot Temporal Logic Optimal Control Synthesis

The majority of existing linear temporal logic (LTL) planning methods rely on the construction of a discrete product automaton, which combines a discrete abstraction of robot mobility and a Büchi automaton that captures the LTL specification. Representing this product automaton as a graph and using graph search techniques, optimal plans that satisfy the LTL task can be synthesized. However, constructing expressive discrete abstractions makes the synthesis problem computationally intractable. In this article, we propose a new sampling-based LTL planning algorithm that does not require any discrete abstraction of robot mobility. Instead, it incrementally builds trees that explore the product state-space, until a maximum number of iterations is reached or a feasible plan is found. The use of trees makes data storage and graph search tractable, which significantly increases the scalability of our algorithm. To accelerate the construction of feasible plans, we introduce bias in the sampling process, which is guided by transitions in the Büchi automaton that belong to the shortest path to the accepting states. We show that our planning algorithm, with and without bias, is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our method outperforms relevant temporal logic planning methods.

Receding Horizon Control-Based Motion Planning With Partially Infeasible LTL Constraints

This work considers online optimal motion planning of an autonomous agent subject to linear temporal logic (LTL) constraints. The environment is dynamic in the sense of containing mobile obstacles and time-varying areas of interest (i.e., time-varying reward and workspace properties) to be visited by the agent. Since user-specified tasks may not be fully realized (i.e., partially infeasible), this work considers hard and soft LTL constraints, where hard constraints enforce safety requirement (e.g. avoid obstacles) while soft constraints represent tasks that can be relaxed to not strictly follow user specifications. The motion planning of the agent is to generate policies, in decreasing order of priority, to 1) formally guarantee the satisfaction of safety constraints; 2) mostly satisfy soft constraints (i.e., minimize the violation cost if desired tasks are partially infeasible); and 3) optimize the objective of rewards collection (i.e., visiting dynamic areas of more interests). To achieve these objectives, a relaxed product automaton, which allows the agent to not strictly follow the desired LTL constraints, is constructed. A utility function is developed to quantify the differences between the revised and the desired motion plan, and the accumulated rewards are designed to bias the motion plan towards those areas of more interests. Receding horizon control is synthesized with an LTL formula to maximize the accumulated utilities over a finite horizon, while ensuring that safety constraints are fully satisfied and soft constraints are mostly satisfied. Simulation and experiment results are provided to demonstrate the effectiveness of the developed motion strategy.

Scalable alignment of process models and event logs: An approach based on automata and S-components

Given a model of the expected behavior of a business process and given an event log recording its observed behavior, the problem of business process conformance checking is that of identifying and describing the differences between the process model and the event log. A desirable feature of a conformance checking technique is that it should identify a minimal yet complete set of differences. Existing conformance checking techniques that fulfill this property exhibit limited scalability when confronted to large and complex process models and event logs. One reason for this limitation is that existing techniques compare each execution trace in the log against the process model separately, without reusing computations made for one trace when processing subsequent traces. Yet, the execution traces of a business process typically share common fragments (e.g. prefixes and suffixes). A second reason is that these techniques do not integrate mechanisms to tackle the combinatorial state explosion inherent to process models with high levels of concurrency. This paper presents two techniques that address these sources of inefficiency. The first technique starts by transforming the process model and the event log into two automata. These automata are then compared based on a synchronized product, which is computed using an A* heuristic with an admissible heuristic function, thus guaranteeing that the resulting synchronized product captures all differences and is minimal in size. The synchronized product is then used to extract optimal (minimal-length) alignments between each trace of the log and the closest corresponding trace of the model. By representing the event log as a single automaton, this technique allows computations for shared prefixes and suffixes to be made only once. The second technique decomposes the process model into a set of automata, known as S-components, such that the product of these automata is equal to the automaton of the whole process model. A product automaton is computed for each S-component separately. The resulting product automata are then recomposed into a single product automaton capturing all the differences between the process model and the event log, but without minimality guarantees. An empirical evaluation using 40 real-life event logs shows that, used in tandem, the proposed techniques outperform state-of-the-art baselines in terms of execution times in a vast majority of cases, with improvements ranging from several-fold to one order of magnitude. Moreover, the decomposition-based technique leads to optimal trace alignments for the vast majority of datasets and close to optimal alignments for the remaining ones.

STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems

This article proposes a new highly scalable and asymptotically optimal control synthesis algorithm from linear temporal logic specifications, called for large-Scale optimal Temporal Logic Synthesis, that is designed to solve complex temporal planning problems in large-scale multi-robot systems. Existing planning approaches with temporal logic specifications rely on graph search techniques applied to a product automaton constructed among the robots. In our previous work, we have proposed a more tractable sampling-based algorithm that builds incrementally trees that approximate the state space and transitions of the synchronous product automaton and does not require sophisticated graph search techniques. Here, we extend our previous work by introducing bias in the sampling process that is guided by transitions in the Büchi automaton that belong to the shortest path to the accepting states. This allows us to synthesize optimal motion plans from product automata with hundreds of orders of magnitude more states than those that existing optimal control synthesis methods or off-the-shelf model checkers can manipulate. We show that is probabilistically complete and asymptotically optimal and has exponential convergence rate. This is the first time that convergence rate results are provided for sampling-based optimal control synthesis methods. We provide simulation results that show that can synthesize optimal motion plans for very large multi-robot systems, which is impossible using state-of-the-art methods.

On-Line Permissive Supervisory Control of Discrete Event Systems for scLTL Specifications

We propose an on-line supervisory control scheme for discrete event systems (DESs), where a control specification is described by a fragment of linear temporal logic. On the product automaton of the DES and an acceptor for the specification, we define a ranking function that returns the minimum number of steps required to reach an accepting state from each state. In addition, we introduce a permissiveness function that indicates a time-varying permissive level. At each step during the on-line control scheme, the supervisor refers to the permissiveness function as well as the ranking function in order to guarantee the control specification while handling the tradeoff between its permissiveness and acceptance of the specification. The proposed scheme is demonstrated in a surveillance problem for a mobile robot.

On-Line Synthesis of Permissive Supervisors for Partially Observed Discrete Event Systems under scLTL Constraints

Abstract We consider a supervisory control problem of a discrete event system (DES) under partial observation, where a control specification is given by a fragment of linear temporal logic We design an on-line supervisor that dynamically computes its control action with the complete information of the product automaton of the DES and an acceptor for the specification. The concepts of controllability and observability are defined by means of a ranking function defined on the product automaton, which decreases its value if an accepting state of the produc automaton is being approached. The proposed on-line control scheme leverages the ranking function and a permissiveness function, which represents a time-varying permissiveness level As a result, the on-line supervisor achieves the specification, being aware of the tradeoff between its permissiveness and acceptance of the specification, if the product automaton is controllable and observable.

Sampling-Based Optimal Control Synthesis for Multirobot Systems Under Global Temporal Tasks

This paper proposes a new optimal control synthesis algorithm for multirobot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton constructed among the robots. In this paper, we propose a new sampling-based algorithm that builds incrementally trees that approximate the state space and transitions of the synchronous product automaton. By approximating the product automaton by a tree rather than representing it explicitly, we require much fewer memory resources to store it and motion plans can be found by tracing sequences of parent nodes without the need for sophisticated graph search methods. This significantly increases the scalability of our algorithm compared to existing optimal control synthesis methods. We also show that the proposed algorithm is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our approach can synthesize optimal plans from product automata with billions of states, which is not possible using standard optimal control synthesis algorithms or model checkers.

Optimal Path Planning Satisfying Complex Task Requirement in Uncertain Environment

SummaryRobots often need to accomplish some complex tasks such as surveillance, response and obstacle avoidance. In this paper, a dynamic search method is proposed to generate optimal robot trajectories satisfying complex task requirement in uncertain environment. The LTL-A* algorithm is presented to generate a global optimal path and the A* algorithm is provided to modify the global optimal path. The task is specified by a linear temporal logic (LTL) formula, and a weighted transition system according to the known information in uncertain environment is modeled to describe the robot motion. Subsequently, a product automaton is constructed by combining the transition system with the task requirement. Based on the product automaton, the LTL-A* algorithm is proposed to generate a global optimal path. The local path planning based on the A* algorithm is employed to deal with the environment change during the process of tracking the global optimal path for the robot. The results of the simulation and experiments show that the proposed method can not only meet the complex task requirement in uncertain environment but also improve the search efficiency.

Control of Magnetic Microrobot Teams for Temporal Micromanipulation Tasks

In this paper, we present a control framework that allows magnetic microrobot teams to accomplish complex micromanipulation tasks captured by global linear temporal logic (LTL) formulas. To address this problem, we propose an optimal control synthesis method that constructs discrete plans for the robots that satisfy both the assigned tasks as well as proximity constraints between the robots due to the physics of the problem. The proposed algorithm relies on an existing optimal control synthesis approach combined with a novel sampling-based technique to reduce the state-space of the product automaton that is associated with the LTL specifications. The synthesized discrete plans are executed by the microrobots independently using local magnetic fields. Simulation studies show that the proposed algorithm can address large-scale planning problems that cannot be solved using existing optimal control synthesis approaches. Moreover, we present experimental results that also illustrate the potential of the method in practice. To the best of our knowledge, this is the first control framework that allows independent control of teams of magnetic microrobots for temporal micromanipulation tasks.

A novel cryptosystem based on cooperating distributed grammar systems

In language theory based cryptography, a block cipher based on Gluškov product of automata was considered and studied. On the other hand the concept of cooperating distributed grammar systems (CDGS) was introduced and studied by Csuhaj-Varjú and Dassow. Motivated by this cryptosystem, we introduce a block cipher based on CDGS which has better security with regard to avalanche effect and is suitable for implementation.

A novel cryptosystem based on cooperating distributed grammar systems

In language theory based cryptography, a block cipher based on Gluskov product of automata was considered and studied. On the other hand the concept of cooperating distributed grammar systems (CDGS) was introduced and studied by Csuhaj-Varju and Dassow. Motivated by this cryptosystem, we introduce a block cipher based on CDGS which has better security with regard to avalanche effect and is suitable for implementation.