Skip to main content Skip to navigation

Publications on decision problems

  • D. Chistikov, R. Majumdar, P. Schepper. Subcubic certificates for CFL reachability. POPL 2022. [doi]

    We show that the lack of truly subcubic algorithms for pushdown reachability is difficult to justify by fine-grained reductions from SAT.

  • D. Chistikov, C. Haase, A. Mansutti. Geometric decision procedures and the VC dimension of linear arithmetic theories. LICS 2022. [WRAP]

    A decision procedure for Presburger arithmetic based on semilinear sets runs in triply exponential time.

  • D. Chistikov, C. Haase, A. Mansutti. Quantifier elimination for counting extensions of Presburger arithmetic. FoSSaCS 2022. [doi]

    We extend linear integer arithmetic with quantifiers of the form “there exists at least c values of x” and similar. It turns out such theories still support efficient quantifier elimination, even in bounded alternation depth.

  • D. Chistikov, C. Haase, Z. Hadizadeh, A. Mansutti. Higher-order Boolean satisfiability. MFCS 2022. To appear.

    We prove that the decision problem for linear arithmetic over Z with just equality (no inequalities) is as hard as for standard linear integer arithmetic. To do so, we define and study the complexity of a quantified version of SAT that supports higher-order Boolean functions.

  • D. Chistikov, S. Kiefer, A. Murawski, D. Purser. The big-O problem. Logical Methods in Computer Science (2022). [doi]

    Given two weighted automata (or labelled Markov chains), is there a constant c such that the weight of every word in the first automaton is at most c times its weight in the second?

  • S. Almagor, D. Chistikov, J. Ouaknine, J. Worrell. O-minimal invariants for discrete-time dynamical systems. ACM Transactions on Computational Logic (2022). Extended version of the ICALP’18 paper. [doi]

    For while loops of the form “while x in S do x:=A*x” (where x is initialized to a rational vector, A is a rational matrix, and S is a nice set), minimal invariants look like truncated cones.

  • D. Chistikov, G. Lisowski, M. Paterson, P. Turrini. Convergence of opinion diffusion is PSPACE-complete. AAAI 2020. [arXiv]

    Suppose in a directed graph each node is coloured 0 or 1. Update colours of all nodes simultaneously, each to the majority among the incoming edges. Does this dynamics converge to a fixed colouring?

  • D. Chistikov, C. Haase. On the power of ordering in linear arithmetic theories. ICALP 2020. [DROPS] [WRAP]

    Given a formula of linear arithmetic, can we decide if the same set can be defined by another formula that uses just equality, without inequalities?

  • D. Chistikov, M. Cadilhac, G. Zetzsche. Rational subsets of Baumslag-Solitar groups. ICALP 2020. [DROPS] [arXiv]

    Imagine a “blind” Turing machine that cannot read bits written on the tape, but can increment a decrement them. The content of the tape is interpreted as the binary expansion of a rational number, and increments and decrements simply add and subtract (possibly negative) powers of two. What sets of numbers do these machines accept?

  • D. Chistikov, S. Kiefer, A. Murawski, D. Purser. The big-O problem for labelled Markov chains and weighted automata. CONCUR 2020. [DROPS] Extended version in Logical Methods in Computer Science (2022).
  • D. Chistikov, P. Martyugin, M. Shirmohammadi. Synchronizing automata over nested words. Journal of Automata, Languages and Combinatorics (2019). Extended version of the FoSSaCS’16 paper. [WRAP]

    We propose a definition of synchronizing words for nested word automata.

  • D. Chistikov, A. Murawski, D. Purser. Asymmetric distances for approximate differential privacy. CONCUR 2019. [DROPS]

    We measure distances between states in labelled Markov chains in the spirit of bisimilarity relation. It turns out that asymmetric distance functions are, in some sense, better.

  • D. Chistikov, C. Haase, S. Halfon. Context-free commutative grammars with integer counters and resets. Theoretical Computer Science (2018). Special issue for RP’14. [WRAP] [arXiv]

    What happens with reachability and coverability sets of VASS where counters can go negative and support reset? Also, a Π2P lower bound on the inclusion problem for linear sets.

  • S. Almagor, D. Chistikov, J. Ouaknine, J. Worrell. O-minimal invariants for linear loops. ICALP 2018. [DROPS] Extended version in ACM Transactions on Computational Logic (2022).
  • D. Chistikov, A. Murawski, D. Purser. Bisimilarity distances for approximate differential privacy. ATVA 2018. [arXiv]

    A pair of states in a labelled Markov chain can be bisimilar or not bisimilar. We extend this equivalence relation to a distance function which upper-bounds the δ parameter in approximate differential privacy.

  • D. Chistikov, R. Dimitrova, R. Majumdar. Approximate counting in SMT and value estimation for probabilistic programs. ACTA Informatica (2017). Special issue for TACAS’15. [WRAP] [arXiv]

    Relying on ideas of Sipser and Stockmeyer, existing SMT solvers can do approximate model counting (discrete counting or volume estimation) for logical theories of arithmetic.

  • D. Chistikov, C. Haase. On the complexity of quantified integer programming. ICALP 2017. [DROPS] [pdf]

    If some variables in integer programs are quantified universally instead of existentially, then the decision problem becomes complete for the k-th level of the polynomial hierarchy, assuming k quantifier blocks.

  • D. Chistikov, S. Kiefer, I. Marušić, M. Shirmohammadi, J. Worrell. On restricted nonnegative matrix factorization. ICALP 2016. [DROPS] [arXiv]

    There exists a pair of 3D polytopes with rational vertices, one inside the other, such that every intermediate polytope with 5 vertices must have a vertex with an irrational coordinate.

  • D. Chistikov, C. Haase. The taming of the semi-linear set. ICALP 2016. [DROPS]

    To measure how semilinear sets “grow” under Boolean operations, we keep track of the maximum norm of generators.

  • D. Chistikov, P. Martyugin, M. Shirmohammadi. Synchronizing automata over nested words. FoSSaCS 2016. Extended version in Journal of Automata, Languages and Combinatorics (2019).
  • D. Chistikov, R. Dimitrova, R. Majumdar. Approximate counting in SMT and value estimation for probabilistic programs. TACAS 2015. Extended version in Acta Informatica (2017).
  • D. Chistikov, R. Majumdar. Unary pushdown automata and straight-line programs. ICALP 2014. [arXiv]

    DPDA equivalence is in P for unary (singleton) input alphabet. This relies on algorithmics for grammar-compressed strings. Also, deciding if a CFG generates words of all lengths is Π2P-complete.