Related papers: Descriptional Complexity of Winning Sets of Regula…
We investigate certain word-construction games with variable turn orders. In these games, Alice and Bob take turns on choosing consecutive letters of a word of fixed length, with Alice winning if the result lies in a predetermined target…
We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…
We study a variant of the synchronization game on finite deterministic automata. In this game, Alice chooses one input letter of an automaton $A$ on each of her moves while Bob may respond with an arbitrary finite word over the input…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
A language $L$ over an alphabet $\Sigma$ is prefix-convex if, for any words $x,y,z\in\Sigma^*$, whenever $x$ and $xyz$ are in $L$, then so is $xy$. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages. We…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
We consider a simple streaming game between two players Alice and Bob, which we call the mirror game. In this game, Alice and Bob take turns saying numbers belonging to the set $\{1, 2, \dots,2N\}$. A player loses if they repeat a number…
Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…
The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all…
We consider the learning and communication complexity of subsequence containment. In the learning problem, we seek to learn a classifier that positively labels a binary string $x$ if it contains a fixed binary string $y$ as a subsequence.…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
Many problems in compositional synthesis and verification of multi-agent systems -- such as rational verification and assume-guarantee verification in probabilistic systems -- reduce to reasoning about two-player multi-objective stochastic…
This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where…
Most natural languages have a predominant or fixed word order. For example in English the word order is usually Subject-Verb-Object. This work attempts to explain this phenomenon as well as other typological findings regarding word order…
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
We consider the permutation analogue of Penney's game for words. Two players, in order, each choose a permutation of length $k\ge3$; then a sequence of independent random values from a continuous distribution is generated, until the…
A language $L$ is the orthogonal catenation of languages $L_1$ and $L_2$ if every word of $L$ can be written in a unique way as a catenation of a word in $L_1$ and a word in $L_2$. We establish a tight bound for the state complexity of…