Emmanuel Filiot

An Antichain Algorithm for LTL Realizability

In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability and synthesis problem. We show how to reduce the LTL realizability problem to a game with an observer that checks that the game visits a bounded number of times accepting states of a universal co-Buchi word automaton. We show that such an observer can be made deterministic and that this deterministic observer has a nice structure which can be exploited by an incremental algorithm that manipulates antichains of game positions. We have implemented this new algorithm and our first results are very encouraging.

Acacia+, a tool for LTL synthesis

We present Acacia+, a tool for solving the LTL realizability and synthesis problems. We use recent approaches that reduce these problems to safety games, and can be solved efficiently by symbolic incremental algorithms based on antichains. The reduction to safety games offers very interesting properties in practice: the construction of compact solutions (when they exist) and a compositional approach for large conjunctions of LTL formulas.

Antichains and compositional algorithms for LTL synthesis

In this paper, we present new monolithic and compositional algorithms to solve the LTL realizability problem. Those new algorithms are based on a reduction of the LTL realizability problem to a game whose winning condition is defined by a universal automaton on infinite words with a k-co-Büchi acceptance condition. This acceptance condition asks that runs visit at most k accepting states, so it implicitly defines a safety game. To obtain efficient algorithms from this construction, we need several additional ingredients. First, we study the structure of the underlying automata constructions, and we show that there exists a partial order that structures the state space of the underlying safety game. This partial order can be used to define an efficient antichain algorithm. Second, we show that the algorithm can be implemented in an incremental way by considering increasing values of k in the acceptance condition. Finally, we show that for large LTL formulas that are written as conjunctions of smaller formulas, we can solve the problem compositionally by first computing winning strategies for each conjunct that appears in the large formula. We report on the behavior of those algorithms on several benchmarks. We show that the compositional algorithms are able to handle LTL formulas that are several pages long.

Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games

We extend the quantitative synthesis framework by going beyond the worst-case. On the one hand, classical analysis of two-player games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees. On the other hand, stochastic models like Markov decision processes represent situations where the system is faced to a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing an higher expected value against a particular stochastic model of the environment given as input. This problem is relevant to produce system controllers that provide nice expected performance in the everyday situation while ensuring a strict (but relaxed) performance threshold even in the event of very bad (while unlikely) circumstances. We study the beyond worst-case synthesis problem for two important quantitative settings: the mean-payoff and the shortest path. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.

Compositional algorithms for LTL synthesis

In this paper, we provide two compositional algorithms to solve safety games and apply them to provide compositional algorithms for the LTL synthesis problem. We have implemented those new compositional algorithms, and we demonstrate that they are able to handle full LTL specifications that are orders of magnitude larger than the specifications that can be treated by the current state of the art algorithms.

Quantitative Languages Defined by Functional Automata

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio. We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. The results on functionality and determinizability are expressed for the more general class of functional group automata. This allows one to formulate within the same framework new results related to discounted sum automata and known results on sum and mean automata. Ratio automata do not fit within this general scheme and different techniques are required to decide functionality.

Regular Transformations of Infinite Strings

The theory of regular transformations of finite strings is quite mature with appealing properties. This class can be equivalently defined using both logic (Monadic second-order logic) and finite-state machines (two-way transducers, and more recently, streaming string transducers); is closed under operations such as sequential composition and regular choice; and problems such as functional equivalence and type checking, are decidable for this class. In this paper, we initiate a study of transformations of infinite strings. The MSO-based definition for regular string transformations generalizes naturally to infinite strings. We define an equivalent generalization of the machine model of streaming string transducers to infinite strings. A streaming string transducer is a deterministic machine that makes a single pass over the input string, and computes the output fragments using a finite set of string variables that are updated in a copyless manner at each step. We show how Muller acceptance condition for automata over infinite strings can be generalized to associate an infinite output string with an infinite execution. The proof that our model captures all MSO-definable transformations uses two-way transducers. Unlike the case of finite strings, MSO-equivalent definition of two-way transducers over infinite strings needs to make decisions based on omega-regular look-ahead. Simulating this look-ahead using multiple variables with copyless updates, is the main technical challenge in our constructions. Finally, we show that type checking and functional equivalence are decidable for MSO-definable transformations of infinite strings.

Quantitative languages defined by functional automata

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio. We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. The results on functionality and determinizability are expressed for the more general class of functional weighted automata over groups. This allows one to formulate within the same framework new results related to discounted sum automata and known results on sum and mean automata. Ratio automata do not fit within this general scheme and specific techniques are required to decide functionality.

From Two-Way to One-Way Finite State Transducers

Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic) characterize the class of regular languages. It is also known that this result does not extend to finite string transductions: (deterministic) two-way finite state transducers strictly extend the expressive power of (functional) one-way transducers. In particular deterministic two-way transducers capture exactly the class of MSO-transductions of finite strings. In this paper, we address the following definability problem: given a function defined by a two-way finite state transducer, is it definable by a one-way finite state transducer? By extending Rabin and Scotts proof to transductions, we show that this problem is decidable. Our procedure builds a one-way transducer, which is equivalent to the two-way transducer, whenever one exists.

TREE AUTOMATA WITH GLOBAL CONSTRAINTS

We define tree automata with global equality and disequality constraints (TAGED). TAGEDs can test (dis)equalities between subtrees which may be arbitrarily faraway. In particular, they are equipped with an equality relation and a disequality relation on states, so that whenever two subtrees t and t′ evaluate (in an accepting run) to two states which are in the (dis)equality relation, they must be (dis)equal. We study several properties of TAGEDs, and prove emptiness decidability of for several expressive subclasses of TAGEDs.