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Wheeler automata were introduced in 2017 as a tool to generalize existing indexing and compression techniques based on the Burrows-Wheeler transform. Intuitively, an automaton is said to be Wheeler if there exists a total order on its…
Synthesis techniques take realizable Linear Temporal Logic specifications and produce correct cir- cuits that implement the specifications. The generated circuits can be used directly, or as miters that check the correctness of a logic…
This paper presents a model-free reinforcement learning (RL) algorithm to synthesize a control policy that maximizes the satisfaction probability of linear temporal logic (LTL) specifications. Due to the consideration of environment and…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
We present a new decision procedure for the logic WS1S. It originates from the classical approach, which first builds an automaton accepting all models of a formula and then tests whether its language is empty. The main novelty is to test…
We propose a control synthesis framework for a heterogeneous multi-robot system to satisfy collaborative tasks, where actions may take varying duration of time to complete. We encode tasks using the discrete logic LTL^\psi, which uses the…
In this paper, we consider the problem of translating LTL formulas to Buechi automata. We first translate the given LTL formula into a special disjuctive-normal form (DNF). The formula will be part of the state, and its DNF normal form…
Autonomous systems often have complex and possibly unknown dynamics due to, e.g., black-box components. This leads to unpredictable behaviors and makes control design with performance guarantees a major challenge. This paper presents a…
Automated algorithm design is entering a new phase: Large Language Models can now generate full optimisation (meta)heuristics, explore vast design spaces and adapt through iterative feedback. Yet this rapid progress is largely…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
We characterize the class of nondeterministic ${\omega}$-automata that can be used for the analysis of finite Markov decision processes (MDPs). We call these automata `good-for-MDPs' (GFM). We show that GFM automata are closed under classic…
Linear temporal logic (LTL) is a compelling framework for specifying complex, structured tasks for reinforcement learning (RL) agents. Recent work has shown that interpreting LTL instructions as finite automata, which can be seen as…
In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to…
We present the first study of non-deterministic weighted automata under probabilistic semantics. In this semantics words are random events, generated by a Markov chain, and functions computed by weighted automata are random variables. We…
Synthesis from linear temporal logic (LTL) specifications provides assured controllers for systems operating in stochastic and potentially adversarial environments. Automatic synthesis tools, however, require a model of the environment to…
Automata over infinite alphabets have emerged as a convenient computational model for processing structures involving data, such as nonces in cryptographic protocols or data values in XML documents. We introduce active learning methods for…
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…
We characterize complete deterministic finite automata with two input letters in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word. The characterization leads to a…
Research in robotic planning with temporal logic specifications, such as Linear Temporal Logic (LTL), has relied on single formulas. However, as task complexity increases, LTL formulas become lengthy, making them difficult to interpret and…