200 research outputs found
Promises Make Finite (Constraint Satisfaction) Problems Infinitary
The fixed template Promise Constraint Satisfaction Problem (PCSP) is a
recently proposed significant generalization of the fixed template CSP, which
includes approximation variants of satisfiability and graph coloring problems.
All the currently known tractable (i.e., solvable in polynomial time) PCSPs
over finite templates can be reduced, in a certain natural way, to tractable
CSPs. However, such CSPs are often over infinite domains. We show that the
infinity is in fact necessary by proving that a specific finite-domain PCSP,
namely (1-in-3-SAT, Not-All-Equal-3-SAT), cannot be naturally reduced to a
tractable finite-domain CSP, unless P=NP
Good-for-games -Pushdown Automata
We introduce good-for-games -pushdown automata (-GFG-PDA).
These are automata whose nondeterminism can be resolved based on the input
processed so far. Good-for-gameness enables automata to be composed with games,
trees, and other automata, applications which otherwise require deterministic
automata. Our main results are that -GFG-PDA are more expressive than
deterministic - pushdown automata and that solving infinite games with
winning conditions specified by -GFG-PDA is EXPTIME-complete. Thus, we
have identified a new class of -contextfree winning conditions for
which solving games is decidable. It follows that the universality problem for
-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties
of the class of languages recognized by -GFG- PDA and decidability of
good-for-gameness of -pushdown automata and languages. Finally, we
compare -GFG-PDA to -visibly PDA, study the resources necessary
to resolve the nondeterminism in -GFG-PDA, and prove that the parity
index hierarchy for -GFG-PDA is infinite.Comment: Extended version of LICS'20 paper of the same name (DOI
10.1145/3373718.3394737); accepted for publication to LMC
Building factorized TAGs with meta-grammars
International audienceHighly compacted TAGs may be built by allowing subtree factorization operators within the elementary trees. While hand-crafting such trees remains possible, a better option arises from a coupling with meta-grammar descriptions. The approach has been validated by the development of FRMG, a wide-coverage French TAG of only 207 trees
Analysis, estimation and control for perturbed and singular systems for systems subject to discrete events.
"The principle investigator for this effort is Professor Alan S. Willsky, and Professor George C. Verghese is co-principal investigator."--P. [3].Includes bibliographical references (p. [20]-[25]).Final technical report for grant AFOSR-88-0032.Supported by the AFOSR. AFOSR-88-003
Homogeneity and Homogenizability: Hard Problems for the Logic SNP
We show that the question whether a given SNP sentence defines a
homogenizable class of finite structures is undecidable, even if the sentence
comes from the connected Datalog fragment and uses at most binary relation
symbols. As a byproduct of our proof, we also get the undecidability of some
other properties for Datalog programs, e.g., whether they can be rewritten in
MMSNP, whether they solve some finite-domain CSP, or whether they define the
age of a reduct of a homogeneous Ramsey structure in a finite relational
signature. We subsequently show that the closely related problem of testing the
amalgamation property for finitely bounded classes is EXPSPACE-hard or
PSPACE-hard, depending on whether the input is specified by a universal
sentence or a set of forbidden substructures.Comment: 34 pages, 3 figure
Algorithms and lower bounds in finite automata size complexity
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 97-99).In this thesis we investigate the relative succinctness of several types of finite automata, focusing mainly on the following four basic models: one-way deterministic (1)FAs), one-way nondeterministic (1NFAs), two-way deterministic (2DFAS), and two-way nondeterministic (2NFAS). First, we establish the exact values of the trade-offs for all conversions from two-way to one-way automata. Specifically, we prove that the functions ... return the exact values of the trade-offs from 2DFAS to 1DFAS, from 2NFAS to 1DFAs, and from 2DFAs or 2NFAS to 1NFAs, respectively. Second, we examine the question whether the trade-offs from NFAs or 2NFAS to 2DiFAs are polynomial or not. We prove two theorems for liveness, the complete problem for the conversion from 1NFAS to 2DFAS. We first focus on moles, a restricted class of 2NFAs that includes the polynomially large 1NFAS which solve liveness. We prove that, in contrast, 2DFA moles cannot solve liveness, irrespective of size.(cont.) We then focus on sweeping 2NFAS, which can change the direction of their input head only on the end-markers. We prove that all sweeping 2NFAs solving the complement of liveness are of exponential size. A simple modification of this argument also proves that the trade-off from 2DFAS to sweeping 2NFAS is exponential. Finally, we examine conversions between two-way automata with more than one head-like devices (e.g., heads, linearly bounded counters, pebbles). We prove that, if the automata of some type A have enough resources to (i) solve problems that no automaton of some other type B can solve, and (ii) simulate any unary 2DFA that has additional access to a linearly-bounded counter, then the trade-off from automata of type A to automata of type B admits no recursive upper bound.by Christos Kapoutsis.Ph.D
Exponential Time Complexity of the Permanent and the Tutte Polynomial
We show conditional lower bounds for well-studied #P-hard problems:
(a) The number of satisfying assignments of a 2-CNF formula with n variables
cannot be counted in time exp(o(n)), and the same is true for computing the
number of all independent sets in an n-vertex graph.
(b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed
in time exp(o(n)).
(c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time
exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it
cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs.
Our lower bounds are relative to (variants of) the Exponential Time
Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF
formulas cannot be decided in time exp(o(n)). We relax this hypothesis by
introducing its counting version #ETH, namely that the satisfying assignments
cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds,
we transfer the sparsification lemma for d-CNF formulas to the counting
setting
Parameter Synthesis in Markov Models: A Gentle Survey
This paper surveys the analysis of parametric Markov models whose transitions
are labelled with functions over a finite set of parameters. These models are
symbolic representations of uncountable many concrete probabilistic models,
each obtained by instantiating the parameters. We consider various analysis
problems for a given logical specification : do all parameter
instantiations within a given region of parameter values satisfy ?,
which instantiations satisfy and which ones do not?, and how can all
such instantiations be characterised, either exactly or approximately? We
address theoretical complexity results and describe the main ideas underlying
state-of-the-art algorithms that established an impressive leap over the last
decade enabling the fully automated analysis of models with millions of states
and thousands of parameters
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