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Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in…
Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative…
Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the n-th level of the hierarchy is over an…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
Constraint Logic Programming (CLP) is a language scheme for combining two declarative paradigms: constraint solving and logic programming. Concurrent Constraint Programming (CCP) is a declarative model for concurrency where agents interact…
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been…
Hankel matrices (aka connection matrices) of word functions and graph parameters have wide applications in automata theory, graph theory, and machine learning. We give a characterization of real-valued functions on nested words recognized…
Decomposable tasks are complex and comprise of a hierarchy of sub-tasks. Spoken intent prediction, for example, combines automatic speech recognition and natural language understanding. Existing benchmarks, however, typically hold out…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
We encode arrays as functions which, in turn, are encoded as sets of ordered pairs. The set cardinality of each of these functions coincides with the length of the array it is representing. Then we define a fragment of set theory that is…
We define compact automata and show that every language has a unique minimal compact automaton. We also define recognition of languages by compact left semitopological monoids and construct the analogue of the syntactic monoid in this…
Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since its…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
In a jumping finite automaton, the input head can jump to an arbitrary position within the remaining input after reading and consuming a symbol. We characterize the corresponding class of languages in terms of special shuffle expressions…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of…
We continue our study of open and closed languages. We investigate how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces;…
Leftist grammars [Motwani et al., STOC 2000] are special semi-Thue systems where symbols can only insert or erase to their left. We develop a theory of leftist grammars seen as word transformers as a tool toward rigorous analyses of their…