Computer Science: Recent submissions
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Halfway to Halfspace Testing
(University of Waterloo, 20171018)In this thesis I study the problem of testing halfspaces under arbitrary probability distributions, using only random samples. A halfspace, or linear threshold function, is a boolean function f : Rⁿ → {±1} defined as the ... 
Quotient Complexity of Bifix, Factor, and Subwordfree Regular Language
(Institute of Informatics: University of Szeged, 2014)A language $L$ is prefixfree if whenever words $u$ and $v$ are in $L$ and $u$ is a prefix of $v$, then $u=v$. Suffix, factor, and subwordfree languages are defined similarly, where by ``subword" we mean ``subsequence", ... 
Complexity of RightIdeal, PrefixClosed, and PrefixFree Regular Languages
(Institute of Informatics: University of Szeged, 2017)A language L over an alphabet E is prefixconvex if, for any words x, y, z is an element of Sigma*, whenever x and xyz are in L, then so is xy. Prefixconvex languages include rightideal, prefixclosed, and prefixfree ... 
Quotient Complexities of Atoms in Regular Ideal Languages
(Institute of Informatics: University of Szeged, 2015)A (left) quotient of a language L by a word w is the language w(1) L = {x vertical bar wx is an element of L}. The quotient complexity of a regular language L is the number of quotients of L; it is equal to the state ... 
The Positive and Negative Influence of Search Results on People's Decisions about the Efficacy of Medical Treatments
(ACM, 20171001)People regularly use web search engines to investigate the efficacy of medical treatments. Search results can contain documents that present incorrect information that contradicts current established medical understanding ... 
In Search Of Most Complex Regular Languages
(World Scientific Publishing, 20130901)Sequences (Ln vertical bar n >= k), called streams, of regular languages Ln are considered, where k is some small positive integer, n is the state complexity of Ln, and the languages in a stream differ only in the ... 
On The Complexity Of The Evaluation Of Transient Extensions Of Boolean Functions
(World Scientific Publishing, 20120101)Transient algebra is a multivalued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions ... 
Quotient Complexity Of StarFree Languages
(World Scientific Publishing, 20120901)The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the ... 
Complexity Of Atoms Of Regular Languages
(World Scientific Publishing, 20131101)The quotient complexity of a regular language L, which is the same as its state complexity the number of left quotients of L. An atom of a nonempty regular language L with n quotients is a nonempty intersection of the n ... 
Most Complex Regular RightIdeal Languages
(Springer, 2014)A right ideal is a language L over an alphabet Sigma that satisfies the equation L = L Sigma*. We show that there exists a sequence (Rn vertical bar n >= 3) of regular rightideal languages, where Rn has n left quotients ... 
Quotient Complexity Of Closed Languages
(Springer, 20140201)A language L is prefixclosed if, whenever a word w is in L, then every prefix of w is also in L. We define suffix, factor, and subwordclosed languages in an analogous way, where by factor we mean contiguous subsequence, ... 
Theory Of Atomata
(Elsevier, 20140619)We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "atomaton", whose states are the "atoms" of the language, that is, nonempty intersections of complemented or ... 
Syntactic Complexity Of R And JTrivial Regular Languages
(World Scientific Publishing, 20141101)The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We ... 
Large Aperiodic Semigroups
(World Scientific Publishing, 20151101)We search for the largest syntactic semigroups of starfree languages having n left quotients; equivalently, we look for the largest transition semigroups of aperiodic finite automata with n states. We first introduce ... 
Syntactic Complexities Of Some Classes Of StarFree Languages
(Springer, 2012)The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of regular languages is the maximal syntactic complexity of languages in that subclass, ... 
Syntactic complexity of suffixfree languages
(Elsevier, 20170905)We solve an open problem concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a suffixfree language with n left quotients (that is, with state complexity n) is at most (n−1)n−2+n−2 ... 
Unrestricted State Complexity Of Binary Operations On Regular And Ideal Languages
(Institut für Informatik, 20170827)We study the state complexity of binary operations on regular languages over diﬀerent alphabets. It is known that if L′m and Ln are languages of state complexities m and n, respectively, and restricted to the same alphabet, ... 
Syntactic Complexity of Regular Ideals
(Springer, 20170804)The state complexity of a regular language is the number of states in a minimal deterministic finite automaton accepting the language. The syntactic complexity of a regular language is the cardinality of its syntactic ... 
Complexity of suffixfree regular languages
(Elsevier, 20171101)We study various complexity properties of suffixfree regular languages. A sequence (Lk,Lk+1,…) of regular languages in some class, where n is the quotient complexity of Ln, is most complex if its languages Ln meet the ... 
Testing Submodularity
(University of Waterloo, 20170928)We show that for any constants $\epsilon > 0$ and $p \ge 1$, given oracle access to an unknown function $f : \{0,1\}^n \to [0,1]$ it is possible to determine if the function is submodular or is $\epsilon$far from every ...