Related papers: On Indexing and Compressing Finite Automata
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
We observe that the classical Cartesian product construction for the intersection of (languages of) nondeterministic finite automata (NFA) is non-optimal in the worst case, if the automata have many transitions. For a fixed alphabet, the…
Minimal deterministic finite automata (DFAs) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
We examine the NFA minimization problem in terms of atomic NFA's, that is, NFA's in which the right language of every state is a union of atoms, where the atoms of a regular language are non-empty intersections of complemented and…
Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…
Efficient pattern matching is fundamental for practical term rewrite engines. By preprocessing the given patterns into a finite deterministic automaton the matching patterns can be decided in a single traversal of the relevant parts of the…
#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical.…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
It was conjectured by \v{C}ern\'y in 1964 that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. In this paper, we…
The Suffix Array is a classic text index enabling on-line pattern matching queries via simple binary search. The main drawback of the Suffix Array is that it takes linear space in the text's length, even if the text itself is extremely…
We study the complexity of basic regular operations on languages represented by incomplete deterministic or nondeterministic automata, in which all states are final. Such languages are known to be prefix-closed. We get tight bounds on both…
We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word…
Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive…
Wheeler DFAs (WDFAs) are a sub-class of finite-state automata which is playing an important role in the emerging field of compressed data structures: as opposed to general automata, WDFAs can be stored in just $\log\sigma + O(1)$ bits per…
It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently.…
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all…
We introduce a measure called width, quantifying the amount of nondeterminism in automata. Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly…
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…