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The correct term is finite sequence because its symbols are ordered and limited in number."},{"text":"finite set","correct":false,"explanation":"A set does not preserve the order or repetition of its elements, both of which matter in strings. A string is therefore a finite sequence of symbols."},{"text":"unordered collection","correct":false,"explanation":"Treating the symbols as unordered loses their positions, so strings such as ab and ba would become indistinguishable. The correct term is finite sequence."}]},{"id":"4251c2eb-7a59-4ec7-b356-618df4754afa","cardType":"basic","points":1,"front":"What does syntax test: form or meaning?","back":"It tests form, not meaning.","mcqOptions":[{"text":"It tests form, not meaning.","correct":true,"explanation":"Syntax concerns whether code or a sentence is structured according to the permitted rules. Meaning is instead considered through semantics."},{"text":"It tests meaning, not form.","correct":false,"explanation":"This reverses syntax and semantics. Syntax tests the form or structure of an expression, whereas semantics concerns what that expression means."},{"text":"It tests form and meaning.","correct":false,"explanation":"Combining the two concepts confuses syntax with semantics. Syntax tests form alone, while separate semantic analysis considers meaning."},{"text":"It tests functionality, not form.","correct":false,"explanation":"Functionality is established through execution and testing rather than syntax analysis. 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A parser primarily checks syntax rules, while later compiler stages may check types and other meaning-related constraints."},{"text":"Whether it uses efficient algorithms.","correct":false,"explanation":"Algorithmic efficiency is assessed through complexity analysis or performance testing, not parsing. A parser checks whether source code follows syntax rules."}]},{"id":"7acc2518-63f2-408a-ba28-fc29dc50715b","cardType":"basic","points":1,"front":"In a grammar, which item appears unchanged in the final string?","back":"A terminal.","mcqOptions":[{"text":"A terminal.","correct":true,"explanation":"Terminals are the actual symbols or tokens of the language. Once produced, they remain unchanged and appear in the completed string."},{"text":"A non-terminal.","correct":false,"explanation":"A non-terminal represents an intermediate grammatical category and must be replaced during derivation. A terminal is the item that remains in the final string."},{"text":"A start symbol.","correct":false,"explanation":"The start symbol begins a derivation and is itself a non-terminal, so it must be expanded. A terminal appears unchanged in the final string."},{"text":"A production rule.","correct":false,"explanation":"A production rule specifies how symbols may be replaced; it is not itself part of the generated string. The unchanged item is a terminal."}]},{"id":"a99e7c2e-782e-4f96-bc20-ef6b5c9739bf","cardType":"basic","points":1,"front":"In a grammar, which item must be expanded into something else?","back":"A non-terminal.","mcqOptions":[{"text":"A non-terminal.","correct":true,"explanation":"Non-terminals name intermediate structures in a grammar. Production rules replace them until the derivation contains only terminals and forms a completed string."},{"text":"A terminal.","correct":false,"explanation":"A terminal is not expanded because it represents a final symbol in the generated string. The item that must be expanded is a non-terminal."},{"text":"A production rule.","correct":false,"explanation":"A production rule performs or specifies an expansion rather than being expanded itself. Non-terminals are the items replaced using those rules."},{"text":"An empty string.","correct":false,"explanation":"The empty string represents a string containing no symbols and is not a grammatical category requiring expansion. A non-terminal must be expanded."}]},{"id":"b062ca5e-b157-4310-9564-35d07005be9e","cardType":"cloze","points":null,"front":"A grammar begins generation from the [ ], which is a non-terminal.","back":"A grammar begins generation from the start symbol, which is a non-terminal.","mcqOptions":[{"text":"start symbol","correct":true,"explanation":"The start symbol is the distinguished non-terminal from which every derivation begins. Production rules are then applied to generate strings in the language."},{"text":"first terminal","correct":false,"explanation":"A terminal is part of a completed generated string and cannot serve as the required initial non-terminal. Generation begins from the start symbol."},{"text":"production rule","correct":false,"explanation":"A production rule describes a permitted replacement, rather than serving as the initial non-terminal. A derivation begins from the start symbol."},{"text":"accepting state","correct":false,"explanation":"An accepting state belongs to finite automata and is not a grammatical symbol used to begin derivations. A grammar begins from its start symbol."}]},{"id":"174b7891-7335-4ee2-9677-ca24f3c3b1ff","cardType":"basic","points":1,"front":"In a context-free grammar, what must be on the left-hand side of each production rule?","back":"A single non-terminal.","mcqOptions":[{"text":"A single non-terminal.","correct":true,"explanation":"A context-free production replaces exactly one non-terminal at a time. Its applicability therefore does not depend on symbols surrounding that non-terminal."},{"text":"A single terminal.","correct":false,"explanation":"Terminals cannot be replaced by production rules in a context-free grammar. The left-hand side must consist of a single non-terminal."},{"text":"A single terminal or non-terminal.","correct":false,"explanation":"Allowing a terminal as an alternative on the left would permit terminals to be rewritten. A context-free rule requires exactly one non-terminal there."},{"text":"A sequence of non-terminals.","correct":false,"explanation":"Requiring several non-terminals would make a rule dependent on surrounding grammatical context. A context-free production has one non-terminal on its left-hand side."}]},{"id":"0057b0fc-4cfb-416f-bb0b-949a32c028ea","cardType":"cloze","points":null,"front":"A language is [ ] if it can be generated by a [ ].","back":"A language is context-free if it can be generated by a context-free grammar.","mcqOptions":[{"text":"A language is context-free if it can be generated by a context-free grammar.","correct":true,"explanation":"Context-free languages are defined precisely as languages generated by context-free grammars, whose production rules each have one non-terminal on the left-hand side."},{"text":"A language is regular if it can be generated by a context-free grammar.","correct":false,"explanation":"Context-free grammars can generate non-regular languages, such as correctly nested brackets. Therefore their generated languages are context-free, not necessarily regular."},{"text":"A language is context-free if it can be generated by a context-sensitive grammar.","correct":false,"explanation":"Context-sensitive grammars are more powerful and can generate languages that are not context-free. A context-free language must be generated by a context-free grammar."},{"text":"A language is finite if it can be generated by a regular grammar.","correct":false,"explanation":"Regular grammars can generate infinite regular languages, so generation by one does not imply that a language is finite. The defining pairing is context-free language and context-free grammar."}]},{"id":"945b63c1-7fef-429b-a0ee-48c1ad1f9dc9","cardType":"basic","points":2,"front":"Why can a context-free rule replace a non-terminal wherever it appears?","back":"It is independent of surrounding symbols.","mcqOptions":[{"text":"It is independent of surrounding symbols.","correct":true,"explanation":"A context-free production depends only on the non-terminal being replaced, not on the symbols before or after it, so it can apply in any surrounding context."},{"text":"It is dependent on adjacent terminals.","correct":false,"explanation":"Dependence on adjacent terminals would make the rule context-sensitive. A context-free rule can replace its non-terminal because it is independent of all surrounding symbols."},{"text":"It is restricted to the starting symbol.","correct":false,"explanation":"Being restricted to the start of a string would prevent replacement wherever the non-terminal occurs. The rule applies because surrounding symbols do not affect it."},{"text":"It is surrounded only by non-terminals.","correct":false,"explanation":"A rule does not require every symbol to be a non-terminal. It can apply wherever its left-hand non-terminal appears because the surrounding context is irrelevant."}]},{"id":"2136baf1-23bf-44b3-beaf-8b498cd1171e","cardType":"cloze","points":null,"front":"In BNF, ::= means [ ], and | means [ ].","back":"In BNF, ::= means is defined as, and | means or.","mcqOptions":[{"text":"In BNF, ::= means is defined as, and | means or.","correct":true,"explanation":"BNF uses ::= to introduce the definition of a non-terminal, while | separates alternative possible productions and is read as “or”."},{"text":"In BNF, ::= means or, and | means is defined as.","correct":false,"explanation":"This reverses the meanings of the two BNF symbols. ::= introduces a definition, while | separates alternatives and means “or”."},{"text":"In BNF, ::= means is assigned to, and | means and.","correct":false,"explanation":"BNF productions describe grammatical alternatives rather than programming assignments and conjunctions. ::= means “is defined as”, and | means “or”."},{"text":"In BNF, ::= means is equal to, and | means divides.","correct":false,"explanation":"These are comparison interpretations borrowed from programming and mathematics, not BNF notation. In BNF, ::= means “is defined as” and | means “or”."}]},{"id":"2ae7250a-e474-4040-9861-47440bb9dc68","cardType":"basic","points":1,"front":"In BNF, how are non-terminals usually written?","back":"In angle brackets, e.g. <digit>.","mcqOptions":[{"text":"In angle brackets, e.g. <digit>.","correct":true,"explanation":"BNF convention encloses non-terminal names in angle brackets, distinguishing grammatical categories such as <digit> from literal terminal symbols in the language."},{"text":"In square brackets, e.g. [digit].","correct":false,"explanation":"Square brackets often indicate optional material in extended grammar notation, not ordinary BNF non-terminals. Non-terminals are conventionally enclosed in angle brackets, as in <digit>."},{"text":"In round brackets, e.g. (digit).","correct":false,"explanation":"Round brackets are commonly used for grouping rather than identifying BNF non-terminals. The usual notation places a non-terminal in angle brackets, such as <digit>."},{"text":"In quotation marks, e.g. “digit”.","correct":false,"explanation":"Quotation marks generally distinguish literal terminal text rather than non-terminal categories. BNF usually writes non-terminals in angle brackets, for example <digit>."}]},{"id":"caa61510-05ef-4335-bb79-bcc55f270794","cardType":"basic","points":1,"front":"In BNF, what makes <identifier> ::= <letter> | <letter><identifier> recursive?","back":"It refers to <identifier> in its own definition.","mcqOptions":[{"text":"It refers to <identifier> in its own definition.","correct":true,"explanation":"The right-hand side includes the same non-terminal that is being defined. This self-reference permits another letter to be added repeatedly before reaching the base case."},{"text":"It refers to <letter> in its own definition.","correct":false,"explanation":"Referring to <letter> does not create recursion because that is a different non-terminal. Recursion comes from <identifier> referring to itself in its definition."},{"text":"It uses the | symbol in its own definition.","correct":false,"explanation":"The alternative symbol offers a choice between productions but does not itself cause recursion. The definition is recursive because its right-hand side contains <identifier>."},{"text":"It contains two alternative productions in its own definition.","correct":false,"explanation":"Having two alternatives does not necessarily make a production recursive. This production is recursive specifically because <identifier> occurs on its own right-hand side."}]},{"id":"32e9dbdf-94e2-4db9-be49-7ad44be350cd","cardType":"basic","points":1,"front":"In BNF, what is recursion mainly used to describe?","back":"Repetition.","mcqOptions":[{"text":"Repetition.","correct":true,"explanation":"A recursive production can invoke itself repeatedly, allowing a grammar to describe structures of variable and potentially unbounded length rather than listing every possible case."},{"text":"Selection.","correct":false,"explanation":"Selection is normally represented by alternative productions separated with |, not by recursion. Recursion is mainly used to express repetition of grammatical structures."},{"text":"Sequencing.","correct":false,"explanation":"Sequencing is expressed by placing symbols consecutively on the right-hand side of a production. Recursion instead allows a pattern to be repeated an arbitrary number of times."},{"text":"Translation.","correct":false,"explanation":"Translation changes a representation or language and is not the main purpose of recursive BNF rules. Recursion primarily describes repeated structures of variable length."}]},{"id":"78bcdfb3-1334-4de9-8d2f-629ea164ac29","cardType":"cloze","points":null,"front":"A derivation repeatedly applies production rules until only [ ] remain.","back":"A derivation repeatedly applies production rules until only terminals remain.","mcqOptions":[{"text":"terminals","correct":true,"explanation":"A derivation is complete when every non-terminal has been replaced through production rules. The remaining terminals form the actual string generated by the grammar."},{"text":"non-terminals","correct":false,"explanation":"Non-terminals are placeholders that must still be expanded, so a derivation has not finished while they remain. A completed derivation contains only terminals."},{"text":"start symbols","correct":false,"explanation":"The start symbol begins a derivation rather than forming its endpoint. It must be expanded until the resulting sequence consists entirely of terminals."},{"text":"production rules","correct":false,"explanation":"Production rules are applied during the derivation but are not symbols in the generated string. The process finishes when only terminal symbols remain."}]},{"id":"4ab5f34f-61c9-441b-8103-e033c8e7a2bd","cardType":"basic","points":1,"front":"When is a string valid under a BNF grammar?","back":"The grammar derives the exact whole string.","mcqOptions":[{"text":"The grammar derives the exact whole string.","correct":true,"explanation":"Validity requires a complete derivation from the grammar’s start symbol that produces every symbol of the candidate string, with no unmatched or additional content."},{"text":"The grammar derives at least one substring.","correct":false,"explanation":"Deriving only a substring does not establish that all input follows the grammar. A valid string must be derived completely and exactly from the start symbol."},{"text":"The grammar contains the same terminal symbols.","correct":false,"explanation":"Sharing terminal symbols with the grammar is insufficient because their order and permitted structure also matter. The grammar must derive the exact whole string."},{"text":"The string begins with a valid terminal symbol.","correct":false,"explanation":"Beginning with a permitted terminal does not guarantee that the rest follows any production. Validity requires the grammar to derive the exact whole string."}]},{"id":"4885e6df-daa4-428d-b2f3-61317a4c099b","cardType":"basic","points":2,"front":"Why is + not a valid signed integer in the example grammar?","back":"After a sign, at least one digit is required.","mcqOptions":[{"text":"After a sign, at least one digit is required.","correct":true,"explanation":"A sign is only an optional prefix to the numeric part; it cannot form an integer alone. The grammar therefore requires one or more digits after it."},{"text":"After a sign, at least one sign is required.","correct":false,"explanation":"A sign need not be followed by another sign, and doing so would not supply a numeric value. The grammar requires at least one digit after the sign."},{"text":"After a sign, at least one decimal point is required.","correct":false,"explanation":"A decimal point would relate to real-number syntax and still would not make + an integer. The signed-integer grammar requires at least one digit after the sign."},{"text":"After a sign, at least one letter is required.","correct":false,"explanation":"A letter would form part of an identifier rather than an integer. To create a signed integer, the grammar requires at least one digit following the sign."}]},{"id":"64695d0d-be67-444f-b9d8-1b6892da09cb","cardType":"cloze","points":null,"front":"In syntax diagrams, branches show [ ], while loops show [ ].","back":"In syntax diagrams, branches show alternatives, while loops show repetition.","mcqOptions":[{"text":"In syntax diagrams, branches show alternatives, while loops show repetition.","correct":true,"explanation":"Branches provide a choice between alternative paths through the syntax, while loops allow part of the path to be followed repeatedly."},{"text":"In syntax diagrams, branches show repetition, while loops show alternatives.","correct":false,"explanation":"This reverses the two conventions. A branch offers alternatives between possible paths, whereas a loop sends the path back to represent repetition."},{"text":"In syntax diagrams, branches show sequencing, while loops show repetition.","correct":false,"explanation":"Sequencing is represented by placing elements consecutively along a path, not by branching. Branches show alternatives, while loops show repetition."},{"text":"In syntax diagrams, branches show alternatives, while loops show termination.","correct":false,"explanation":"Termination is shown by reaching the diagram’s exit rather than by a loop. Branches represent alternatives, and loops represent repetition."}]},{"id":"167fd2fc-2ae0-4f17-ad2c-62ef9263a84f","cardType":"basic","points":2,"front":"Why is a- invalid in the identifier syntax diagram?","back":"- cannot match <letter>, and cannot be left over.","mcqOptions":[{"text":"- cannot match <letter>, and cannot be left over.","correct":true,"explanation":"After a matches the required letter, the hyphen cannot match the diagram’s next permitted symbol. Valid parsing must consume the entire input."},{"text":"a cannot match <letter>, so the diagram rejects immediately.","correct":false,"explanation":"The initial a is a letter and therefore matches <letter>. The failure occurs because the remaining hyphen matches no permitted symbol and cannot be left unconsumed."},{"text":"- can match <letter>, but only before another letter.","correct":false,"explanation":"The hyphen does not match <letter> at any position. The identifier is invalid because parsing must consume every character, including the final hyphen."},{"text":"- matches <letter>, but identifiers must end in a digit.","correct":false,"explanation":"The diagram does not impose a rule that identifiers must finish with digits. The hyphen is rejected because it cannot match <letter> or remain unconsumed."}]},{"id":"446acea7-64a3-4d83-97d9-65cfdd47622f","cardType":"cloze","points":null,"front":"Regular expressions cannot generally enforce unlimited [ ] or [ ].","back":"Regular expressions cannot generally enforce unlimited matching pairs or nesting.","mcqOptions":[{"text":"Regular expressions cannot generally enforce unlimited matching pairs or nesting.","correct":true,"explanation":"Matching arbitrarily many corresponding symbols and tracking arbitrarily deep nested structures require unbounded memory, which ordinary regular expressions and finite automata lack."},{"text":"Regular expressions cannot generally enforce unlimited matching pairs or repetition.","correct":false,"explanation":"Regular expressions can enforce unlimited repetition using operators such as Kleene star. Their limitation is enforcing linked matching pairs or arbitrarily deep nesting."},{"text":"Regular expressions cannot generally enforce unlimited alternation or nesting.","correct":false,"explanation":"Alternation is a basic regular-expression operation, so it is not the limitation. Regular expressions generally cannot enforce unlimited matching pairs or nesting."},{"text":"Regular expressions cannot generally enforce unlimited repetition or optionality.","correct":false,"explanation":"Repetition and optionality are directly expressible with regular-expression operators. The genuine limitations are unlimited matching pairs and arbitrarily deep nesting."}]},{"id":"56945fa3-63dc-4c82-93d8-32551a7a70a5","cardType":"basic","points":2,"front":"In <S> ::= a<S>b | ab, what does each recursive expansion add?","back":"One a at the front and one b at the end.","mcqOptions":[{"text":"One a at the front and one b at the end.","correct":true,"explanation":"Applying a<S>b replaces <S> with a new form surrounded by one leading a and one trailing b."},{"text":"One a at the front and two bs at the end.","correct":false,"explanation":"The recursive production places exactly one a before <S> and one b after it. It does not add two trailing bs."},{"text":"One b at the front and one a at the end.","correct":false,"explanation":"The symbols have been reversed. In a<S>b, the a is added before the recursive non-terminal and the b after it."},{"text":"One a and one b both at the end.","correct":false,"explanation":"The production surrounds the existing non-terminal rather than appending both symbols. Each expansion adds one a at the front and one b at the end."}]},{"id":"817fbb01-bf5e-4748-be2f-c18febea66e5","cardType":"basic","points":2,"front":"Why is a*b* insufficient for a^n b^n?","back":"It can match unequal counts, e.g. abb.","mcqOptions":[{"text":"It can match unequal counts, e.g. abb.","correct":true,"explanation":"Each Kleene star independently permits any number of its symbol, so nothing forces the number of as to equal the number of bs."},{"text":"It requires at least one of each symbol, e.g. ab.","correct":false,"explanation":"The stars permit zero occurrences, so neither symbol is compulsory. More importantly, they choose the numbers of as and bs independently rather than making them equal."},{"text":"It can match symbols in either order, e.g. ba.","correct":false,"explanation":"The expression actually keeps all as before all bs. Its failure is that the two stars can select unequal counts, such as in abb."},{"text":"It can match only equal counts, e.g. aabb.","correct":false,"explanation":"This confuses independent repetition with linked repetition. The two stars do not coordinate their counts, so a*b* also accepts strings such as abb."}]}]}],"examCountdown":{"examDate":"2027-05-11","paperLabel":"Paper 1"},"heading":"Context-free languages","title":"Context-free languages Flashcards","topbar":{"backHref":"/as-level/computer-science/aqa/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"72418042-1f54-5a48-83b5-efe418142f37","walled":"$L38"}],"$L39","$L3a"]