Formal Languages and Automata Theory
In this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin's seminal \LStar\ algorithm works when the semiring is a principal ideal domain, but not for general semirings such…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
Every function on a finite set defines an equivalence relation and, therefore, a partition called the kernel of the function. Automata such that every possible partition is the kernel of a word are called totally compatible. A…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is a FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides…
We propose an automaton model which is a combination of symbolic and register automata, i.e., we enrich symbolic automata with memory. We call such automata Symbolic Register Automata (SRA). SRA extend the expressive power of symbolic…
We consider a system consisting of a sequential composition of Mealy machines, called head and tail. We study two problems related to these systems. In the first problem, models of both head and tail components are available, and the aim is…
In the Intersection Non-Emptiness problem, we are given a list of finite automata $A_1,A_2,\dots,A_m$ over a common alphabet $\Sigma$ as input, and the goal is to determine whether some string $w\in \Sigma^*$ lies in the intersection of the…
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…
For every fixed class of regular languages, there is a natural hierarchy of increasingly more general problems: Firstly, the membership problem asks whether a given language belongs to the fixed class of languages. Secondly, the separation…
Abelian repetition threshold ART(k) is the number separating fractional Abelian powers which are avoidable and unavoidable over the k-letter alphabet. The exact values of ART(k) are unknown; the lower bounds were proved in [A.V. Samsonov,…
In this paper, we give a Nivat-like characterization for weighted alternating automata over commutative semirings (WAFA). To this purpose we prove that weighted alternating can be characterized as the concatenation of weighted finite tree…
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…
We study the problem of synthesizing implementations from temporal logic specifications that need to work correctly in all environments that can be represented as transducers with a limited number of states. This problem was originally…
Temporal logic is often used to describe temporal properties in AI applications. The most popular language for doing so is Linear Temporal Logic (LTL). Recently, LTL on finite traces, LTLf, has been investigated in several contexts. In…
This volume contains the proceedings of the 12th International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2021). The aim of GandALF 2021 symposium is to bring together researchers from academia and industry which…
Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification.…
In the classical synthesis problem, we are given an LTL formula \psi over sets of input and output signals, and we synthesize a system T that realizes \psi: with every input sequences x, the system associates an output sequence T(x) such…
For general input automata, there exist regular constraint languages such that asking if a given input automaton admits a synchronizing word in the constraint language is PSPACE-complete or NP-complete. Here, we investigate this problem for…
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…
In today's world, critical infrastructure is often controlled by computing systems. This introduces new risks for cyber attacks, which can compromise the security and disrupt the functionality of these systems. It is therefore necessary to…