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...ly implemented in logic families like [[CMOS]] and [[Transistor–transistor logic|TTL]]. They are [[Duality_(mathematics)#Duality_in_logic_and_set_theory|dua {{Logic-stub}} ...

...''', is a system for proving [[classical logic|classical]] [[propositional logic|propositional]] tautologies. * [[Completeness (logic)|Completeness]]: every propositional [[tautology (logic)|tautology]] has a ''P''-proof, ...

...ounding principles''', and '''least number principles''' are three related families of first-order principles, which may or may not hold in [[Non-standard mode Informally, for a [[First-order logic|first-order]] [[Well-formed formula|formula]] of arithmetic <math>\varphi(x ...

...eralization of [[Boolean circuits]] and a mathematical model for digital [[logic circuits]]. Circuits are defined by the gates they contain and the values t ...integers where the circuit <math>C_n</math> has <math>n</math> variables. Families of circuits can thus be seen as functions from <math>M^{*}</math> to <math> ...

...will not explore all of these states in finite time. For several important families of systems such as [[pushdown systems]], [[channel systems]] or [[counter s ...ion| title=Proc. 4th Int. Symp. on Programming Language Implementation and Logic Programming (PLILP)|date=Aug 1992| volume=631| pages=269–296| publisher=Spr ...

...the unrelated usage of these words for [[universal quantifier]]s in the [[logic of graphs]], and for [[apex graph]]s. ==In special families of graphs== ...

...ion with the [[GNRS conjecture]] on metric embedding of minor-closed graph families, the <math>k</math>-outerplanar graphs are one of the most general classes ...h by finite state tree automata is definable in the monadic second-order [[logic of graphs]], has been proven for the <math>k</math>-outerplanar graphs.<ref ...

...2}}.</ref><ref>{{citation | title=Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach | volume=138 | series=Encyclopedia of Mathem | title = The monadic second-order logic of graphs. I. Recognizable sets of finite graphs ...

cite arXiv| title =Node polynomials for families: results and examples| ...= Bullock| first3 = Igor L.| last3 = Markov| title = Synthesis of quantum logic circuits | journal = [[IEEE Transactions on Computer-Aided Design of Integr ...

...d '''equivalent''' if <math>M \leq N</math> and <math>N \leq M.</math> The families <math>M</math> and <math>N</math> are '''comparable''' if one of these sets If two families of sets <math>M</math> and <math>N</math> are equivalent then either both < ...

...ete graph]]s. A variation of twin-width, ''sparse twin-width'', applies to families of graphs rather than to individual graphs. For a family of graphs that is ...bounded [[queue number]] also has bounded twin-width.{{r|tw2}} There exist families of graphs of bounded sparse twin-width that do not have bounded stack numbe ...

...to structural decompositions of matroids, and characterizations of matroid families by forbidden minors, analogous to the corresponding theory in graphs. Many important families of matroids are closed under the operation of taking minors: if a matroid ' ...

...is uniform between the Simon implementations; however, the key generation logic is dependent on the implementation of 2, 3 or 4 keys. ...f rounds:<ref name=eprintSimon>{{cite conference|title=The Simon and Speck Families Of Lightweight Block Ciphers |url=http://eprint.iacr.org/2013/404.pdf |work ...

...f [[abstract simplicial complex]]es on a set with <math>n</math> elements, families of sets with the property that any non-empty subset of a set in the family | title = Finite and Infinite Combinatorics in Sets and Logic (Proc. NATO Advanced Study Inst., Banff, Alberta, Canada, May 4, 1991) ...

==Related graph families== | title = The logic engine and the realization problem for nearest neighbor graphs ...

...individual vertices and edges of a graph, while monadic second-order graph logic allows quantification over sets of vertices or edges. Logics based on [[lea ...at a [[random graph]] has a property specified within a particular type of logic, and methods for [[data compression]] based on finding logical sentences th ...

...subset of the limiting support of ''P_n''. By the aforementioned logic, this statement is also false. | title = Locally asymptotically normal families of distributions ...

...h> to <math>x</math> and commutes with exponentiation and sums of summable families in <math>F^{LE}_{\omega}</math> lying in <math>F_{\omega}</math>. ...xponential-logarithmic and logarithmic-exponential series''], Mathematical Logic Quarterly, 2012</ref> ...

==Related families of graphs== | journal = [[Archive for Mathematical Logic]] ...

| series = Studies in Logic and the Foundations of Mathematics [[Category:Parametric families of graphs]] ...