In formal language theory, a context-free language is a language generated by a context-free grammar. Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language; the set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing. Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar, though going the other way is not as direct. A model context-free language is L =, the language of all non-empty even-length strings, the entire first halves of which are a's, the entire second halves of which are b's. L is generated by the grammar S → a S b | a b.
This language is not regular. It is accepted by the pushdown automaton M = where δ is defined as follows: δ = δ = δ = δ = δ = Unambiguous CFLs are a proper subset of all CFLs: there are inherently ambiguous CFLs. An example of an inherently ambiguous CFL is the union of with; this set is context-free. But there is no way to unambiguously parse strings in the subset, the intersection of these two languages; the language of all properly matched parentheses is generated by the grammar S → S S | | ε. The context-free nature of the language makes it simple to parse with a pushdown automaton. Determining an instance of the membership problem. Context-free recognition for Chomsky normal form grammars was shown by Leslie G. Valiant to be reducible to boolean matrix multiplication, thus inheriting its complexity upper bound of O. Conversely, Lillian Lee has shown O boolean matrix multiplication to be reducible to O CFG parsing, thus establishing some kind of lower bound for the latter. Practical uses
Wood drying reduces the moisture content of wood before its use. When the drying is done in a kiln, the product is known as kiln-dried timber or lumber, whereas air drying is the more traditional method. There are two main reasons for drying wood: Woodworking When wood is used as a construction material, whether as a structural support in a building or in woodworking objects, it will absorb or desorb moisture until it is in equilibrium with its surroundings. Equilibration causes unequal shrinkage in the wood, can cause damage to the wood if equilibration occurs too rapidly; the equilibration must be controlled to prevent damage to the wood. Wood burning When wood is burned, it is best to dry it first. Damage from shrinkage is not a problem here, as it may be in the case of drying for woodworking purposes. Moisture affects the burning process, with unburnt hydrocarbons going up the chimney. If a 50% wet log is burnt at high temperature, with good heat extraction from the exhaust gas leading to a 100 °C exhaust temperature, about 5% of the energy of the log is wasted through evaporating and heating the water vapour.
With condensers, the efficiency can be further increased. For some purposes, wood is not dried at all, is used green. Wood must be in equilibrium with the air outside, as for construction wood, or the air indoors, as for wooden furniture. Wood dried in a purpose built oven; the wood is sawn before drying, but sometimes the log is dried whole. Case hardening describes lumber or timber, dried too rapidly. Wood dries from the shell, shrinking the shell and putting the core under compression; when this shell is at a low moisture content it will resist shrinkage. The core of the wood is still at a higher moisture content; this core will begin to dry and shrink. However, any shrinkage is resisted by the already'set' shell; this leads to reversed stresses. This results in unrelieved stress called case hardening. Case-hardened may warp and dangerously when the stress is released by sawing. Wood is divided, according to its botanical origin, into two kinds: softwoods, from coniferous trees, hardwoods, from broad-leaved trees.
Softwoods are lighter and simple in structure, whereas hardwoods are harder and more complex. However, in Australia, softwood describes rain forest trees, hardwood describes Sclerophyll species. Softwoods such as pine are much lighter and easier to process than hardwoods such as fruit tree wood; the density of softwoods ranges from 350 kg/m3 to 700 kg/m3, while hardwoods are 450 kg/m3 to 1250 kg/m3. Once dried, both consist of 12% of moisture; because of hardwood's denser and more complex structure, its permeability is much less than that of softwood, making it more difficult to dry. Although there are about a hundred times more species of hardwood trees than softwood trees, the ability to be dried and processed faster and more makes softwood the main supply of commercial wood today; the timber of living trees and fresh logs contains a large amount of water which constitutes over 50% of the wood's weight. Water has a significant influence on wood. Wood continually exchanges moisture or water with its surroundings, although the rate of exchange is affected by the degree to which wood is sealed.
Wood contains water in three forms: Free water The bulk of water contained in the cell lumina is only held by capillary forces. It is called free water. Free water is not in the same thermodynamic state as liquid water: energy is required to overcome the capillary forces. Furthermore, free water may contain chemicals. Bound or hygroscopic water Bound; the attraction of wood for water arises from the presence of free hydroxyl groups in the cellulose and lignin molecules in the cell wall. The hydroxyl groups are negatively charged; because water is a polar liquid, the free hydroxyl groups in cellulose attract and hold water by hydrogen bonding. Vapor Water in cell lumina in the form of water vapour is negligible at normal temperature and humidity; the moisture content of wood is calculated as the mass change as a proportion of the dry mass, by the formula: moisture content = m g − m od m od × 100 % Here, m g is the green mass of the wood, m od is its oven dry mass. The equation can be expressed as a fraction of the mass of the water and the mass of the oven dry wood rather than a percentage.
For example, 0.59 kg/kg expresses the same moisture content as 59%. When green wood dries, free water from the cell lumina, held by the capillary forces only, is the first to go. Physical properties, such as strength and shrinkage, are not affected by the removal of free water; the fibre saturation point is defined as the moisture content at which free water should be gone
The 1964 United States presidential election in Georgia took place on November 3, 1964, as part of the 1964 United States presidential election, held on that day throughout all 50 states and The District of Columbia. Voters chose 12 representatives, or electors to the Electoral College, who voted for president and vice president; this would mark the first time that Georgia was carried by the Republican nominee on a presidential election. During the 1960s the Deep South was in a state of turmoil due to upheavals resulting from the Civil Rights Movement; the Democratic Party had traditionally been the defender of white supremacy and segregation in the South, but since acquiring the support of northern blacks in the 1930s, wartime race riots in Detroit, the ascendancy of Henry A. Wallace to the vice presidency its left wing had become strong supporters of moves to restore black political rights in the former Confederacy; the growth of protests and marches demanding black civil rights in the region early in the 1960s led the reluctant John F. Kennedy to submit "sweeping Civil Rights legislation to Congress".
Following Kennedy's assassination, new President Lyndon Johnson, although a Southerner, felt he had to act with Civil Rights legislation, which produced the Civil Rights Act of July 1964. The independence of county governance from the state legislature, the large number of counties in the state, produced a split in policy between areas in and north of Atlanta versus the south of the state. In the south of Georgia, local officials behaved to those of Mississippi and organised large-scale, violent "massive resistance" to desegregation and voter registration by blacks. Although Governor Carl Sanders endorsed Johnson, was bitterly critical of Republican nominee, Arizona Senator Barry Goldwater's belief that "extremism in the defense of liberty is no vice", he was alone among Georgia's leading officials in doing so. Most state politicians, led by James H. Gray preferred Goldwater because of his vote against the Civil Rights Act, as did Calvin F. Craig, who headed Georgia's powerful Ku Klux Klan, because he saw the election as battle between Goldwater's "Americanism" and Johnson's "socialism".
A "Democrats for Goldwater" group was organized by the "Citizens' Council". The majority of opinion polls between July and early October suggested that, despite this widespread opposition to Johnson's programs, Goldwater would not take the Peach State. In fact, in early August, Georgia was viewed as alongside Arkansas and North Carolina as the most secure southern state for Johnson; those Democratic Party delegates who refused to support Goldwater because of his policies on rural electrification and subsidies to tobacco farmers were concerned that Goldwater could carry Georgia – and the entire South – as early as late August. Moreover, in Valdosta in the far south, the region where resistance to black civil rights was most extreme, white union workers in September had been polled as supporting Goldwater 315 to 19, with 1 vote for George Wallace who would carry the state in 1968. By the end of September, it was clear that the state was bitterly divided, with the rock-solid Democratic south rooting for Goldwater but defections from Republican support during the previous election in the northern counties appearing to be as widespread, because there was some hope Johnson could reverse large population declines and entrenched poverty.
By the end of October, amidst much campaigning in the state by both Johnson and Goldwater, it was thought Georgia was leaning towards the Republicans. As it turned out Georgia joined Mississippi, South Carolina and Louisiana in supporting the Arizona senator as a protest against the Civil Rights Act, although it did so by a smaller margin – 8.25% – than any other Deep South state Goldwater carried. Over-representation of urban areas in polling was blamed for this discrepancy. Compared to the previous election, Georgia swung to the Republicans by over 34%, though this masked enormous regional differences. Among the rural areas of the "black belt" and the south of the state, there were enormous swings to Goldwater as the whites – the only people who voted – deserted Johnson. For instance, Miller County went from 94% for Kennedy to only 14% for Johnson, Lee County from 69% for Kennedy to only 19 percent for Johnson. In contrast, only 55% of those Georgian voters who supported Nixon in 1960 remained with Goldwater.
Deserting of the Republicans in pro-Union and entirely white Appalachia gave Towns County to the Democrats for the first time since 1952, nearly switched Gilmer and Pickens Counties. Illustrating the "bifurcated" political change in the state was that whilst FDR carried the state by 83.83 percentage points in 1932, Herbert Hoover had won Towns County by 48 votes. One of the best examples of Pro-Unionists going to Democrats was Long County, which had only given Kennedy 23 percent of the vote in 1960, but gave Johnson 84% in 1964. Goldwater's victory in Georgia in 1964 was the Republican Party's first victory in the state in any presidential election; this was an incredible feat given that Goldwater lost to Lyndon B. Johnson in a landslide; the Peach State had long been a Democratic stronghold, which it would remain, Presidential elections aside, well into the 1990s. Between 1852 and 1960, Georgia had supported the Democratic Presidential nominee in every election with the sole exception of 1864, when Georgia had seceded from the Union.
However, from this election onward, the Peach State has supported Democrats only three times, two of those occurred when Georgia native Jimmy Carter was on the ballot (while fellow southern Democrat Bill Clinton would do so the third, to this day, the most recent time when Georgia v