Related papers: Testing the Equivalence of Regular Languages
Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
Automatic measures of similarity between utterances are invaluable for training speech synthesizers, evaluating machine translation, and assessing learner productions. While there exist measures for semantic similarity and prosodic…
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…
While many applications of automata in formal methods can use nondeterministic automata, some applications, most notably synthesis, need deterministic or good-for-games (GFG) automata. The latter are nondeterministic automata that can…
An automaton is synchronizing if there is a word that maps all states onto the same state. \v{C}ern\'{y}'s conjecture on the length of the shortest such word is probably the most famous open problem in automata theory. We consider the…
This is a tutorial on finite automata. We present the standard material on determinization and minimization, as well as an account of the equivalence of finite automata and monadic second-order logic. We conclude with an introduction to the…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
"Quantitative languages are extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the…
Probabilistic automata were introduced by Rabin in 1963 as language acceptors. Two automata are equivalent if and only if they accept each word with the same probability. On the other side, in the process algebra community, probabilistic…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
We present an algorithm that takes an unannotated corpus as its input, and returns a ranked list of probable morphologically related pairs as its output. The algorithm tries to discover morphologically related pairs by looking for pairs…
A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it…
Autoformalization aims to convert informal mathematical proofs into machine-verifiable formats, bridging the gap between natural and formal languages. However, ensuring semantic alignment between the informal and formalized statements…
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…
We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.
This paper situates itself in the theory of variable length codes and of finite automata where the concepts of completeness and synchronization play a central role. In this theoretical setting, we investigate the problem of finding upper…
Co-lex partial orders were recently introduced in (Cotumaccio et al., SODA 2021 and JACM 2023) as a powerful tool to index finite state automata, with applications to regular expression matching. They generalize Wheeler orders (Gagie et…
Query term matching with document term matching is the basic function of any best effort Information Retrieval models like Vector Space Model. In our problem of SMS based Information Systems we expect common people to participate in…
A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by S\'enizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for…