The idea of automatic synthesis of reactive programs starting from temporal logic (LTL) specifications is quite old, but was commonly thought to be infeasible due to the known double exponential complexity of the problem. However, new ideas have recently renewed the interest in LTL synthesis: One major new contribution in this area is the recent work of Piterman et al. who showed how polynomial time synthesis can be achieved for a large class of LTL specifications that is expressive enough to cover many practical examples. These LTL specifications are equivalent to omega-automata having a so-called GR(1) acceptance condition. This approach has been used to automatically synthesize implementations of real-world applications. To this end, manually written deterministic omega-automata having GR(1) conditions were used instead of the original LTL specifications. However, manually generating deterministic monitors is, of course, a hard and error-prone task. In this paper, we therefore present algorithms to automatically translate specifications of a remarkable large fragment of LTL to deterministic monitors having a GR(1) acceptance condition so that the synthesis algorithms can start with more readable LTL specifications.
Temporal synthesis is the automated design of a system that interacts with an environment, using the declarative specification of the system's behavior. A popular language for providing such a specification is Linear Temporal Logic, or LTL. LTL synthesis in the general case has remained, however, a hard problem to solve in practice. Because of this, many works have focused on developing synthesis procedures for specific fragments of LTL, with an easier synthesis problem. In this work, we focus on Safety LTL, defined here to be the Until-free fragment of LTL in Negation Normal Form~(NNF), and s…
We present the Temporal Logic Synthesis Format (TLSF), a high-level format to describe synthesis problems via Linear Temporal Logic (LTL). The format builds upon standard LTL, but additionally allows to use high level constructs, such as sets and functions, to provide a compact and human readable representation. Furthermore, the format allows to identify parameters of a specification such that a single description can be used to define a family of problems. We also present a tool to automatically translate the format into plain LTL, which then can be used for synthesis by a solver. The tool al…
We present the Temporal Logic Synthesis Format (TLSF), a high-level format to describe synthesis problems via Linear Temporal Logic (LTL). The format builds upon standard LTL, but additionally allows to use high-level constructs, such as sets and functions, to provide a compact and human-readable representation. Furthermore, the format allows to identify parameters of a specification such that a single description can be used to define a family of problems. Additionally, we present a tool to automatically translate the format into plain LTL, which then can be used for synthesis by a solver. Th…
We classify the complexity of the LTL satisfiability and model checking problems for several standard parameterisations. The investigated parameters are temporal depth, number of propositional variables and formula treewidth, resp., pathwidth. We show that all operator fragments of LTL under the investigated parameterisations are intractable in the sense of parameterised complexity.
LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics…
The synthesis of reactive systems from linear temporal logic (LTL) specifications is an important aspect in the design of reliable software and hardware. We present our adaption of the classic automata-theoretic approach to LTL synthesis, implemented in the tool Strix which has won the two last synthesis competitions (Syntcomp2018/2019). The presented approach is (1) structured, meaning that the states used in the construction have a semantic structure that is exploited in several ways, it performs a (2) forward exploration such that it often constructs only a small subset of the reachable sta…
Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidabl…
We consider the synthesis of distributed implementations for specifications in Prompt Linear Temporal Logic (PROMPT-LTL), which extends LTL by temporal operators equipped with parameters that bound their scope. For single process synthesis it is well-established that such parametric extensions do not increase worst-case complexities. For synchronous systems, we show that, despite being more powerful, the distributed realizability problem for PROMPT-LTL is not harder than its LTL counterpart. For asynchronous systems we have to consider an assume-guarantee synthesis problem, as we have to expre…
We reduce synthesis for CTL* properties to synthesis for LTL. In the context of model checking this is impossible - CTL* is more expressive than LTL. Yet, in synthesis we have knowledge of the system structure and we can add new outputs. These outputs can be used to encode witnesses of the satisfaction of CTL* subformulas directly into the system. This way, we construct an LTL formula, over old and new outputs and original inputs, which is realisable if, and only if, the original CTL* formula is realisable. The CTL*-via-LTL synthesis approach preserves the problem complexity, although it might…
Extended Bounded Response LTL with Past (LTLEBR+P) is a safety fragment of Linear Temporal Logic with Past (LTL+P) that has been recently introduced in the context of reactive synthesis. The strength of LTLEBR+P is a fully symbolic compilation of formulas into symbolic deterministic automata. Its syntax is organized in four levels. The first three levels feature (a particular combination of) future temporal modalities, the last one admits only past temporal operators. At the base of such a structuring there are algorithmic motivations: each level corresponds to a step of the algorithm for the …
Rice University（莱斯大学）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
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 tra…
LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial intelligence applications. In this research note we consider De Giacomo and Vardi's variant of the synthesis problem for LTL formulas interpreted over finite rather than infinite traces. Rather surprisingly, given the existing claims on complexity, we establish that LTL synthesis is EXPTIME-complete for the finite interpretation, and not 2EXPTIME-complete as previous…
Each China Normal University（华东师范大学）；Sapienza Università di Roma（罗马大学）；Rice University（莱斯大学）
In synthesis, assumptions are constraints on the environment that rule out certain environment behaviors. A key observation here is that even if we consider systems with LTLf goals on finite traces, environment assumptions need to be expressed over infinite traces, since accomplishing the agent goals may require an unbounded number of environment action. To solve synthesis with respect to finite-trace LTLf goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTLf and in LTL have the same worst-case complexity (both 2EXPTIME-com…
The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL m…
We consider the synthesis of distributed implementations for specifications in parameterized temporal logics such as PROMPT-LTL, which extends LTL by temporal operators equipped with parameters that bound their scope. For single process synthesis it is well-established that such parametric extensions do not increase worst-case complexities. For synchronous distributed systems we show that, despite being more powerful, the realizability problem for PROMPT-LTL is not harder than its LTL counterpart. For asynchronous systems we have to express scheduling assumptions and therefore consider an assu…
In the classical synthesis problem, we are given an LTL formula psi over sets of input and output signals, and we synthesize a transducer that realizes psi. One weakness of automated synthesis in practice is that it pays no attention to the quality of the synthesized system. Indeed, the classical setting is Boolean: a computation satisfies a specification or does not satisfy it. Accordingly, while the synthesized system is correct, there is no guarantee about its quality. In recent years, researchers have considered extensions of the classical Boolean setting to a quantitative one. The logic L…
CISPA Helmholtz Center for Information Security（CISPA 赫尔姆霍兹信息安全中心）；University of Antwerp – Flanders Make Antwerp（安特卫普大学 - 弗拉芒制造安特卫普）；EPITA Research Laboratory（EPITA 研究实验室）
Reactive synthesis builds a system from a specification given as a temporal logic formula. Traditionally, reactive synthesis is defined for systems with Boolean input and output variables. Recently, new theories and techniques have been proposed to extend reactive synthesis to data domains, which are required for more sophisticated programs. In particular, Temporal stream logic(TSL) (Finkbeiner et al. 2019) extends LTL with state variables, updates, and uninterpreted functions and was created for use in synthesis. We present a synthesis procedure for TSL(T), an extension of TSL with theories. …
Reactive synthesis is a key technique for the design of correct-by-construction systems and has been thoroughly investigated in the last decades. It consists in the synthesis of a controller that reacts to environment's inputs satisfying a given temporal logic specification. Common approaches are based on the explicit construction of automata and on their determinization, which limit their scalability. In this paper, we introduce a new fragment of Linear Temporal Logic, called Extended Bounded Response LTL (\LTLEBR), that allows one to combine bounded and universal unbounded temporal operators…
We introduce a new approach for the synthesis of Mealy machines from specifications in linear-time temporal logic (LTL), where the number of cycles in the state graph of the implementation is limited by a given bound. Bounding the number of cycles leads to implementations that are structurally simpler and easier to understand. We solve the synthesis problem via an extension of SAT-based bounded synthesis, where we additionally construct a witness structure that limits the number of cycles. We also establish a triple-exponential upper and lower bound for the potential blow-up between the length…
University of Toronto（多伦多大学）；CNRS（法国国家科学研究中心）；Univ. Montpellier（蒙彼利埃大学）；Inria（法国国家信息与自动化研究所）
In this paper, we investigate the problem of synthesizing strategies for linear temporal logic (LTL) specifications that are interpreted over finite traces -- a problem that is central to the automated construction of controllers, robot programs, and business processes. We study a natural variant of the finite LTL synthesis problem in which strategy guarantees are predicated on specified environment behavior. We further explore a quantitative extension of LTL that supports specification of quality measures, utilizing it to synthesize high-quality strategies. We propose new notions of optimalit…
We study the realizability problem for Safety LTL, the syntactic fragment of Linear Temporal Logic capturing safe formulas. We show that the problem is EXP-complete, disproving the existing conjecture of 2EXP-completeness. We achieve this by comparing the complexity of Safety LTL with seemingly weaker subfragments. In particular, we show that every formula of Safety LTL can be reduced to an equirealizable formula of the form $α\land \Box ψ$, where $α$ is a present formula over system variables and $ψ$ contains Next as the only temporal operator. The realizability problem for this new fragment,…
University of Pennsylvania（宾夕法尼亚大学）；Rice University（莱斯大学）；Tesla（特斯拉）
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.…
We study a variant of the problem of synthesizing Mealy machines that enforce LTL specifications against all possible behaviours of the environment including hostile ones. In the variant studied here, the user provides the high level LTL specification ϕ of the system to design, and a set E of examples of executions that the solution must produce. Our synthesis algorithm works in two phases. First, it generalizes the decisions taken along the examples E using tailored extensions of automata learning algorithms. This phase generalizes the user-provided examples in E while preserving realizabilit…
We study satisfiability for HyperLTL with a $\forall^*\exists^*$ quantifier prefix, known to be highly undecidable in general. HyperLTL can express system properties that relate multiple traces (so-called hyperproperties), which are often combined with trace properties that specify functional behavior on single traces. Following this conceptual split, we first define several safety and liveness fragments of $\forall^*\exists^*$ HyperLTL, and characterize the complexity of their (often much easier) satisfiability problem. We then add LTL trace properties as functional specifications. Though (hi…
Automatic synthesis from temporal logic specifications is an attractive alternative to manual system design, due to its ability to generate correct-by-construction implementations from high-level specifications. Due to the high complexity of the synthesis problem, significant research efforts have been directed at developing practically efficient approaches for restricted specification language fragments. In this paper, we focus on the Safety LTL fragment of Linear Temporal Logic (LTL) syntactically extended with bounded temporal operators. We propose a new synthesis approach with the primary …
We propose "semantic labelling" as a novel ingredient for solving games in the context of LTL synthesis. It exploits recent advances in the automata-based approach, yielding more information for each state of the generated parity game than the game graph can capture. We utilize this extra information to improve standard approaches as follows. (i) Compared to strategy improvement (SI) with random initial strategy, a more informed initialization often yields a winning strategy directly without any computation. (ii) This initialization makes SI also yield smaller solutions. (iii) While Q-learning…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Synthesizing a program that realizes a logical specification is a classical problem in computer science. We examine a particular type of program synthesis, where the objective is to synthesize a strategy that reacts to a potentially adversarial environment while ensuring that all executions satisfy a Linear Temporal Logic (LTL) specification. Unfortunately, exact methods to solve so-called LTL synthesis via logical inference do not scale. In this work, we cast LTL synthesis as an optimization problem. We employ a neural network to learn a Q-function that is then used to guide search, and to co…
Decision-making policies for agents are often synthesized with the constraint that a formal specification of behaviour is satisfied. Here we focus on infinite-horizon properties. On the one hand, Linear Temporal Logic (LTL) is a popular example of a formalism for qualitative specifications. On the other hand, Steady-State Policy Synthesis (SSPS) has recently received considerable attention as it provides a more quantitative and more behavioural perspective on specifications, in terms of the frequency with which states are visited. Finally, rewards provide a classic framework for quantitative p…
Given a specification of linear-time temporal logic interpreted over finite traces (LTLf), the reactive synthesis problem asks to find a finitely-representable, terminating controller that reacts to the uncontrollable actions of an environment in order to enforce a desired system specification. In this paper we study, for the first time, the reactive synthesis problem for DECLARE - a fragment of LTLf extensively used both in theory and practice for specifying declarative, constraint-based business processes. We provide a threefold contribution. First, we give a naive, doubly exponential time s…
We present a new algorithm to construct a deterministic Rabin automaton for an LTL formula $φ$. The automaton is the product of a master automaton and an array of slave automata, one for each $G$-subformula of $φ$. The slave automaton for $Gψ$ is in charge of recognizing whether $FGψ$ holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows to apply various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compa…
