Related papers: Undecidability and Finite Automata
The complexity and decidability of various decision problems involving the shuffle operation are studied. The following three problems are all shown to be $NP$-complete: given a nondeterministic finite automaton (NFA) $M$, and two words $u$…
Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the…
We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the…
We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games.
The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field,…
We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
We study the seeded domino problem, the recurring domino problem and the $k$-SAT problem on finitely generated groups. These problems are generalization of their original versions on $\mathbb{Z}^2$ that were shown to be undecidable using…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
We establish several results on the word problem for just infinite groups. First, for finitely generated just infinite groups we show that the word problem is uniformly decidable for presentations with recursively enumerable sets of…
The analogue of Hilbert's tenth problem over $\mathbb{Q}$ asks for an algorithm to decide the existence of rational points in algebraic varieties over this field. This remains as one of the main open problems in the area of undecidability…
Register automata are finite automata equipped with a finite set of registers ranging over the domain of some relational structure like $(\mathbb N;=)$ or $(\mathbb Q;<)$. Register automata process words over the domain, and along a run of…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…
We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given k-automatic sequence is ultimately…
Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MM-QFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we…
We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy…