Related papers: Regular realizability problems and regular languag…
Several new algorithms for deciding emptiness of Boolean combinations of regular languages and of languages of alternating automata (AFA) have been proposed recently, especially in the context of analysing regular expressions and in string…
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…
We introduce the problem of temporal coverability for realizability and synthesis. Namely, given a language of words that must be covered by a produced system, how to automatically produce such a system. We consider the case of coverability…
Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…
Several reachability problems in finite automata, such as completeness of NFAs and synchronisation of total DFAs, correspond to fundamental properties of sets of nonnegative matrices. In particular, the two mentioned properties correspond…
The Int_reg-problem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_reg-problem for a number of…
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as…
The problems of \emph{verification} and \emph{realizability} are two central themes in the analysis of reactive systems. When multiagent systems are considered, these problems have natural analogues of existence (nonemptiness) of…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
The problem DFA-Intersection-Nonemptiness asks if a given number of deterministic automata accept a common word. In general, this problem is PSPACE-complete. Here, we investigate this problem for the subclasses of commutative automata and…
Regular model checking is a well-established technique for the verification of regular transition systems (RTS): transition systems whose initial configurations and transition relation can be effectively encoded as regular languages. In…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular…
We investigate the computational complexity of various problems for simple recurrent neural networks (RNNs) as formal models for recognizing weighted languages. We focus on the single-layer, ReLU-activation, rational-weight RNNs with…
We show that testing inclusion between languages represented by regular expressions with numerical occurrence indicators (RE#s) is NP-hard, even if the expressions satisfy the requirement of "unambiguity", which is required for XML Schema…
We initiate a complexity theoretic study of the language based graph reachability problem (L-REACH) : Fix a language L. Given a graph whose edges are labeled with alphabet symbols of the language L and two special vertices s and t, test if…
Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular,…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…