Better logic obeying a zero-one law
نویسندگان
چکیده
We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P , is there a language of graphs able to express P while obeying the zeroone law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey the zero-one law. On the other hand we show that in any (semiregular) language strong enough to express Hamiltonicity one can interpret arithmetic and thus the zero-one law fails miserably. This answers a question of Blass and Harary.
منابع مشابه
"Politics as a Virtue" In the Idea of Feyz-e- Kashani
Mullah Mohsen Faiz-e-Kashani (996-1077 AH) is one of the great Imami thinkers in the second period of the Safavid dynasty in Iran, who is influenced by two views of Sadra and Hadith’s philosophy. He has presented his thoughts on politics by relying on the traditions of the Ahl al-Bayt (PBUT) and focusing on the virtues of Islamic philosophy. Thus, the main question of this article is how Feyz-e...
متن کاملZero-One Law for Regular Languages and Semigroups with Zero
A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular language has the zero-one law if and only if its syntactic monoid has a zero element. Our proof gives both algebraic and automata characterisation of the zero-one l...
متن کاملZero-One Law and Rational Quantifiers
We study extensions of finite variable logic Lω ∞ω by generalized quantifiers. We use strong version of so-called extension axioms and pebble games to show the zero-one law for the obtained logic. In some cases we show that the zero-one law does not hold by constructing a sentence with no limit probability. We construct these sentences with as few variables as possible and thus find the exact n...
متن کاملStrong extension axioms and Shelah's zero-one law for choiceless polynomial time
This paper developed from Shelah's proof of a zero-one law for the complexity class \choiceless polynomial time," de ned by Shelah and the authors. We present a detailed proof of Shelah's result for graphs, and describe the extent of its generalizability to other sorts of structures. The extension axioms, which form the basis for earlier zero-one laws (for rst-order logic, xed-point logic, and ...
متن کاملOn The Geometry of Equilibrium Solutions of Kinetic Systems Obeying the Mass Action Law ⋆
In this contribution the problem relating dynamic behavior and parameter values for weakly reversible chemical reaction networks (CRNs) that obey the mass action law is revisited. The approach is founded on previous methods and results discussed in [15, 16] for weakly reversible CRNs. Two new research directions are however undertaken in this study, one of them exploits an alternative factoriza...
متن کامل