REPORTS > KEYWORD > LOGIC:
Reports tagged with logic:
TR98-067 | 12th November 1998
Paul Beame

#### Propositional Proof Complexity: Past, Present and Future

Proof complexity, the study of the lengths of proofs in
propositional logic, is an area of study that is fundamentally connected
both to major open questions of computational complexity theory and
to practical properties of automated theorem provers. In the last
decade, there have been a number of significant advances ... more >>>

TR03-024 | 25th February 2003
Till Tantau

#### Weak Cardinality Theorems for First-Order Logic

Kummer's cardinality theorem states that a language is recursive
if a Turing machine can exclude for any n words one of the
n + 1 possibilities for the number of words in the language. It
is known that this theorem does not hold for polynomial-time
computations, but there ... more >>>

TR06-021 | 10th February 2006
Tomas Feder

#### Constraint satisfaction: a personal perspective

Attempts at classifying computational problems as polynomial time
solvable, NP-complete, or belonging to a higher level in the polynomial
hierarchy, face the difficulty of undecidability. These classes, including
NP, admit a logic formulation. By suitably restricting the formulation, one
finds the logic class MMSNP, or monotone monadic strict NP without
more >>>

TR06-160 | 17th December 2006
Tomas Feder, Phokion G. Kolaitis

#### Closures and dichotomies for quantified constraints

Quantified constraint satisfaction is the generalization of
constraint satisfaction that allows for both universal and existential
of just existential quantifiers.
We study quantified constraint satisfaction problems ${\rm CSP}(Q,S)$, where $Q$ denotes
a pattern of quantifier alternation ending in exists or the set of all possible
more >>>

TR09-111 | 5th November 2009
Walid Gomaa

#### Model-Theoretic Characterization of Complexity Classes

Model theory is a branch of mathematical logic that investigates the
logical properties of mathematical structures. It has been quite
successfully applied to computational complexity resulting in an
area of research called descriptive complexity theory. Descriptive
complexity is essentially a syntactical characterization of
complexity classes using logical formalisms. However, there ... more >>>

TR11-158 | 25th November 2011
Matthew Anderson, Dieter van Melkebeek, Nicole Schweikardt, Luc Segoufin

#### Locality from Circuit Lower Bounds

We study the locality of an extension of first-order logic that captures graph queries computable in AC$^0$, i.e., by families of polynomial-size constant-depth circuits. The extension considers first-order formulas over relational structures which may use arbitrary numerical predicates in such a way that their truth value is independent of the ... more >>>

TR12-069 | 23rd March 2012
Lakhdar Saïs, Mohand-Saïd Hacid, francois hantry

#### On the complexity of computing minimal unsatisfiable LTL formulas

We show that (1) the Minimal False QCNF search problem (MF-search) and
the Minimal Unsatisfiable LTL formula search problem (MU-search) are FPSPACE complete because of the very expressive power of QBF/LTL, (2) we extend the PSPACE-hardness of the MF decision problem to the MU decision problem. As a consequence, we ... more >>>

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