Related papers: Transition Complexity of Incomplete DFAs
With the growing diversity of instruction set architectures (ISAs), cross-ISA program execution has become common. Dynamic binary translation (DBT) is the main solution but suffers from poor performance. Cross-compilation avoids emulation…
We study the state complexity of boolean operations, concatenation and star with one or two of the argument languages reversed. We derive tight upper bounds for the symmetric differences and differences of such languages. We prove that the…
It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…
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 $u$…
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the…
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…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic…
We study the emptiness and $\lambda$-reachability problems for unary and binary Probabilistic Finite Automata (PFA) and characterise the complexity of these problems in terms of the degree of ambiguity of the automaton and the size of its…
Regular expressions provide a flexible means for matching strings and they are often used in data-intensive applications. They are formally equivalent to either deterministic finite automata (DFAs) or nondeterministic finite automata…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input…
In this work we construct an automaton for the commutative closure of a given regular group language. The number of states of the resulting automaton is bounded by the number of states of the original automaton, raised to the power of the…
Automatic structures are infinite structures that are finitely represented by synchronized finite-state automata. This paper concerns specifically automatic structures over finite words and trees (ranked/unranked). We investigate the…
We present a new characteristic of a regular ideal language called reset complexity. We find some bounds on the reset complexity in terms of the state complexity of a given language. We also compare the reset complexity and the state…
We investigate the state complexity of the shuffle operation on regular languages initiated by Campeanu et al. and studied subsequently by Brzozowski et al. We shift the problem into the combinatorics domain by turning the problem of state…
When their reading heads are allowed to move completely asynchronously, finite-state automata with multiple tapes achieve a significant expressive power, but also lose useful closure properties---closure under intersection, in particular.…
In this work, we introduce DeepDFA, a novel approach to identifying Deterministic Finite Automata (DFAs) from traces, harnessing a differentiable yet discrete model. Inspired by both the probabilistic relaxation of DFAs and Recurrent Neural…