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- Dmitry Chistikov, Rayna Dimitrova, Rupak Majumdar
- Acta Informatica
- 2015

#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)

- Dmitry Chistikov, Rupak Majumdar
- ICALP
- 2014

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)

- Dmitry Chistikov, Pavel Martyugin, Mahsa Shirmohammadi
- FoSSaCS
- 2016

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 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)

- UDC, D. V. Chistikov, S. E. Bubnov
- 2013

We prove a universal upper bound on checking test length for read-once functions over the elementary basis. We also identify the exact value of the corresponding Shannon function for the basis of conjunction and disjunction. A checking test problem for read-once functions, also known as testing with respect to read-once alternatives, was set up by A. A.… (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. Restricted NMF requires in addition that the column spaces of M and W coincide. Finding the minimal inner dimension d is known to be NP-hard, both for NMF and restricted NMF.… (More)

- Dmitry Chistikov, Christoph Haase
- ICALP
- 2016

Semi-linear sets, which are finitely generated subsets of the monoid (Z d , +), have numerous applications in theoretical computer science. Although semi-linear sets are usually given implicitly, by formulas in Presburger arithmetic or by other means, the effect of Boolean operations on semi-linear sets in terms of the size of generators has primarily been… (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)

- Dmitry Chistikov
- IWOCA
- 2011

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)

- Dmitry Chistikov
- FSTTCS
- 2014

We determine the descriptional complexity (smallest number of states, up to constant factors) of recognizing languages {1 n } and {1 tn : t = 0, 1, 2,. . .} with state-based finite machines of various kinds. This task is understood as counting to n and modulo n, respectively, and was previously studied for classes of finite-state automata by Kupferman,… (More)