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#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of satisfiability modulo theories (SMT) there is a growing need for model counting solvers, coming from several application domains… (More)

A checking test for a monotone read-once function f depending essentially on all its n variables is a set of vectors M distinguishing f from all other monotone read-once functions of the same variables. We describe an inductive procedure for obtaining individual lower and upper bounds on the minimal number of vectors T (f) in a checking test for any… (More)

We extend the concept of a synchronizing word from finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i.e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it… (More)

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality)… (More)

We show that any one-counter automaton with n states, if its language is non-empty, accepts some word of length at most O(n 2). This closes the gap between the previously known upper bound of O(n 3) and lower bound of Ω(n 2). More generally, we prove a tight upper bound on the length of shortest paths between arbitrary configurations in one-counter… (More)

We study the class of relations implemented by nested word to word transducers (also known as visibly pushdown transducers). We show that any such relation can be uniformized by a functional relation from the same class, implemented by an unambiguous transducer. We give an exponential upper bound on the state complexity of the uniformization, improving a… (More)

—The concept of a checking test is of prime interest to the study of a variant of exact identification problem, in which the learner is given a hint about the unknown object. A graph F is said to be a checking test for a cograph G iff for any other cograph H there exists an edge in F distinguishing G and H, that is, contained in exactly one of the graphs G… (More)

We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L(A): its (1) downward closure, (2) upward closure, or (3) Parikh image. For the Parikh image over a fixed alphabet and for the… (More)

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are… (More)