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### k-Subgraph Isomorphism on AC0 Circuits

Kazuyuki Amano
2010 Computational Complexity
In this paper, we study the complexity of the k-subgraph isomorphism problem on constant-depth circuits.  ...  the constant-depth circuit complexity for detecting a pattern H (of a fixed size k) of O(n t+1 log n) where t is the treewidth of H.  ...  Suppose that constant-depth circuits of size O(n t ) compute HypClique n ,k , where t = s − 2k s / k .  ...

### On the (Non) NP-Hardness of Computing Circuit Complexity

Cody D. Murray, R. Ryan Williams, Marc Herbstritt
2015 Computational Complexity Conference
The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size parameter k, is the circuit complexity of f at most k?  ...  We also consider the nondeterministic generalization of MCSP: the Nondeterministic Minimum Circuit Size Problem (NMCSP), where one wishes to compute the nondeterministic circuit complexity of a given function  ...  A simple lemma on the circuit complexity of substrings We also use the fact that for any string T , the circuit complexity of an arbitrary substring of T can be bounded via the circuit complexity of T  ...

### Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC0

Sorin Istrail, Dejan Zivkovic
1994 Information Processing Letters
We show that the complexity classes AC0 and NC' consist exactly of, respectively, constant and O(log n) width polynomial-size Boolean formulas.  ...  Introduction The complexity classes AC? and NC' and their modifications are well studied in the literature. For example, Furst et al.  and independently Ajtai [ 1 ] proved that AC0 # NC'.  ...  Definitions In this section we review some of the basic notions from Boolean circuit complexity (for more details see, for example, [ 61 and [ 31).  ...

### Patterns hidden from simple algorithms

2011 Communications of the ACM
More things appear random to simpler, or resource-limited, algorithms than to complex, powerful, algorithms. And why should we care? Because randomness is a key resource in computation.  ...  Only recently, Bazzi  resolved a special case of the conjecture (for the case of AC0 functions corresponding to depth 2 circuits, or "DNF formulae").  ...  AC0 functions are those whose input-output behavior can be described by a Boolean logic circuit consisting n input wires and polynomially many NOT gates and AND and OR gates of arbitrary fan-in.  ...

### Algorithms for Circuits and Circuits for Algorithms

Ryan Williams
2014 2014 IEEE 29th Conference on Computational Complexity (CCC)
The title of this paper is meant to highlight an emerging duality between two fundamental topics in algorithms and complexity theory.  ...  Algorithms for circuits refers to the design of interesting algorithms which can perform non-trivial circuit analysis of some kind, on either a circuit or a Boolean function given as a truth table.  ...  (It is known that SETH implies ETH.) 9 AC0-SAT: The next more expressive class of circuits is AC0, with arbitrary constant depth.  ...

### Review—Nonlinear Electrochemical Impedance Spectroscopy

Fathima Fasmin, Ramanathan Srinivasan
2017 Journal of the Electrochemical Society
Complex reactions.  ...  F,N L (E ac0 ) = R p,N L (E ac0 ) + R sol = lim ω→0 Z T [4b] If the actual reaction is a simple electron transfer reaction in the kinetic controlled regime, then the complex plane plot of the impedance  ...

### Effect of potential drifts and ac amplitude on the electrochemical impedance spectra

S. Noyel Victoria, S. Ramanathan
2011 Electrochimica Acta
It is shown that if the data were to be analyzed without validation by KKT, it can lead to incorrect choice of reaction mechanism or equivalent circuits.  ...  V ac0 = 10 mV(original data) V ac0 = 10 mV(transformed result) V ac0 = 100 mV(original data) V ac0 = 100 mV(transformed result) Complex plane plots of impedance spectra for direct dissolution under stable  ...  Vdrift = 0.01V Vdrift = 0.01V V ac0 =10 mV (original data) Vac0= 0.1V_KKT V ac0 =10 mV (transformed result) Complex plane plots of impedance spectra for dissolution with one adsorbed intermediate species  ...

### Numerical investigations of solution resistance effects on nonlinear electrochemical impedance spectra

Sruthi Santhanam, Vimala Ramani, Ramanathan Srinivasan
2011 Journal of Solid State Electrochemistry
Electrical circuits with negative resistances and capacitances were used to simulate the impedance spectra with data in the second quadrant of the complex plane plots .  ...  Fig. 7 7 shows the complex plane plots of impedance for V ac0 = 10 mV, for various solution resistance values.  ...

### Detection of nonlinearities in electrochemical impedance spectra by Kramers–Kronig Transforms

Fathima Fasmin, Ramanathan Srinivasan
2015 Journal of Solid State Electrochemistry
(b) Complex plane plots of impedance spectra V ac0 = 1 mV and 300 mV, inset shows the expanded view of V ac0 = 300 mV low frequency data.  ...  (a) Figure captions Complex plane plots of impedance spectra V ac0 = 1 mV and 300 mV. Bode plots of (c) |Z| and (d) Φ at V ac0 = 300 mV.  ...

### Regular languages in NC1

David A. Mix Barrington, Kevin Compton, Howard Straubing, Denis Thérien
1992 Journal of computer and system sciences (Print)
We give several characterizations, in terms of formal logic, semigroup theory, and operations on languages, of the regular languages in the circuit complexity class AC', thus answering a question of Chandra  ...  We also obtain logical characterizations for the class of all languages recognized by nonuniform circuit families in which mod m gates (where m is not necessarily prime) are permitted.  ...  Indeed, any regular language in AC0 can be recognized by a highly uniform AC0 circuit family.  ...

### A note on some languages in uniform ACC0

David A. Mix Barrington, James Corbett
1991 Theoretical Computer Science
ACC" (also called ACC) is the class of languages recognized by circuit families with polynomial size, constant depth, and u?  ...  circuit for L,. This being impossible, we can conclude that no family of AC0 circuits exists for L,.  ...  fan-in two and depth O(Iog n)-see  for an overview of circuit complexity theory).  ...

### An analysis of drifts and nonlinearities in electrochemical impedance spectra

Niket S. Kaisare, Vimala Ramani, Karthik Pushpavanam, S. Ramanathan
2011 Electrochimica Acta
The inset shows the low frequency impedance for V ac0 of 200 mV, expanded for clarity X V ac0 = 1 mV V ac0 = 10 mV V ac0 = 100 mV V ac0 = 200 mV Fig. 8 .Fig 9 . 89 Complex plane plots of impedance spectra  ...  The charge stabilized are presented as complex plane plots infig. 8. Again, the impedance values for V ac0 = 1 mV and 10 mV are identical.  ...

### On uniformity within NC1

David A. Mix Barrington, Neil Immerman, Howard Straubing
1990 Journal of computer and system sciences (Print)
We show that these two notions are equivalent, leading to a natural notion of uniformity for low-level circuit complexity classes.  ...  In order to study circuit complexity classes within NC' in a uniform setting, we need a uniformity condition which is more restrictive than those in common use.  ...  We will now define our basic circuit complexity classes in their non-uniform versions.  ...

### Queries with arithmetical constraints

Stéphane Grumbach, Jianwen Su
1997 Theoretical Computer Science
We first consider the data complexity of first-order queries.  ...  We prove in particular that linear queries can be evaluated in AC0 over finite integer databases, and in NC' over linear constraint databases. This improves previously known bounds.  ...  We consider classical complexity classes based on Turing machines such as LOGSPACE and PTIME, classes based on Boolean circuits, with AND, OR, and NEG gates, such as AC0 with constant depth, a polynomial  ...

### Fusion trees can be implemented with AC0 instructions only

Arne Andersson, Peter Bro Miltersen, Mikkel Thorup
1999 Theoretical Computer Science
The AC0 instructions used are not all available on today's computers. @ 1999-Elsevier Science B.V.  ...  Addressing a problem of Fredman and Willard, we implement fusion trees in deterministic linear space using AC0 instructions only.  ...  Fredman and Willard point out that multiplication is not an AC0 instruction, that is, there are no circuits for multiplication of constant depth and of size (number of gates) polynomial in the word length  ...
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