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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Least fixpoints as meanings of recursive definitions.
ContextFree Languages and PushDown Automata
 Handbook of Formal Languages
, 1997
"... Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : ..."
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Cited by 62 (0 self)
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Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.1 Grammars : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2. Systems of equations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.1 Systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Resolution : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 2.3 Linear systems : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.4 Parikh's theorem : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
COMPLEXITY OF SOLUTIONS OF EQUATIONS OVER SETS OF NATURAL NUMBERS
, 2008
"... Systems of equations over sets of natural numbers (or, equivalently, language equations over a oneletter alphabet) of the form Xi = ϕi(X1,..., Xn) (1 � i � n) are considered. Expressions ϕi may contain the operations of union, intersection and pairwise sum A+B = {x+y  x ∈ A, y ∈ B}. A system with ..."
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Systems of equations over sets of natural numbers (or, equivalently, language equations over a oneletter alphabet) of the form Xi = ϕi(X1,..., Xn) (1 � i � n) are considered. Expressions ϕi may contain the operations of union, intersection and pairwise sum A+B = {x+y  x ∈ A, y ∈ B}. A system with an EXPTIMEcomplete least solution is constructed, and it is established that least solutions of all such systems are in EXPTIME. The general membership problem for these equations is proved to be EXPTIMEcomplete.
Generalised reduction modified LR parsing for domain specific language prototyping
 Proc. 35th Annual Hawaii International Conference On System Sciences (HICSS02), IEEE Computer Society
, 2002
"... Domain specific languages should support syntax that is comfortable for specialist users. We discuss the impact of the standard deterministic parsing techniques such as LALR(1) and LL(1) on the design of programming languages and the desirability of more flexible parsers in a development environment ..."
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Cited by 5 (1 self)
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Domain specific languages should support syntax that is comfortable for specialist users. We discuss the impact of the standard deterministic parsing techniques such as LALR(1) and LL(1) on the design of programming languages and the desirability of more flexible parsers in a development environment. We present a new bottomup nondeterministic parsing algorithm (GRMLR) that combines a modified notion of reduction with a Tomitastyle breadthfirst search of parallel parsing stacks. We give experimental results for standard programming language grammars and LR(0), SLR(1) and LR(1) tables; the weaker tables generate significant amounts of nondeterminism. We show that GRMLR parsing corrects errors in the standard Tomita algorithm without incurring the performance overheads associated with other published solutions. We also demonstrate that the performance of GRMLR is upperbounded by the performance of Tomita’s algorithm, and that for one realistic language grammar GRMLR only needs to search around 74 % of the nodes. Our heavily instrumented development version of the algorithm achieves parsing rates of around 4,000–10,000 tokens per second on a 400MHz Pentium II processor. Proof of correctness and details of our implementation are omitted here for space reasons but are available in an accompanying technical report.
Strict language inequalities and their decision problems
 Mathematical Foundations of Computer Science (MFCS 2005
, 2005
"... Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an ..."
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Abstract. Systems of language equations of the form {ϕ(X1,..., Xn) = ∅, ψ(X1,..., Xn) � = ∅} are studied, where ϕ, ψ may contain settheoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X1,..., Xn) ⊂ L0. It is proved that the problem whether such an inequality has a solution is Σ2complete, the problem whether it has a unique solution is in (Σ3 ∩Π3)\(Σ2 ∪Π2), the existence of a regular solution is a Σ1complete problem, while testing whether there are finitely many solutions is Σ3complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached. 1
Abstract interpretation of algebraic polynomial systems (Extended Abstract)
 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY, AMAST ’97
, 1997
"... We define a hierarchy of compositional formal semantics of algebraic polynomial systems over Falgebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flowanalysis algorithms in the same uniform framework of universal algebra and ..."
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We define a hierarchy of compositional formal semantics of algebraic polynomial systems over Falgebras by abstract interpretation. This generalizes classical formal language theoretical results and contextfree grammar flowanalysis algorithms in the same uniform framework of universal algebra and abstract interpretation.
EQUATIONS OVER SETS OF NATURAL NUMBERS WITH ADDITION ONLY
, 2009
"... Systems of equations of the form X = Y Z and X = C are considered, in which the unknowns are sets of natural numbers, “+ ” denotes pairwise sum of sets S+T = {m + n  m ∈ S, n ∈ T}, and C is an ultimately periodic constant. It is shown that such systems are computationally universal, in the sense t ..."
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Cited by 2 (2 self)
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Systems of equations of the form X = Y Z and X = C are considered, in which the unknowns are sets of natural numbers, “+ ” denotes pairwise sum of sets S+T = {m + n  m ∈ S, n ∈ T}, and C is an ultimately periodic constant. It is shown that such systems are computationally universal, in the sense that for every recursive (r.e., cor.e.) set S ⊆ N there exists a system with a unique (least, greatest) solution containing a component T with S = {n  16n + 13 ∈ T}. This implies undecidability of basic properties of these equations. All results also apply to language equations over a oneletter alphabet with concatenation and regular constants.
An extension of recursive descent parsing for Boolean grammars
"... The wellknown recursive descent parsing method for contextfree grammars is extended for their generalization, Boolean grammars, which include explicit settheoretic operations in the formalism of rules. Conjunction is implemented by scanning a part of the input multiple times, while the mechanism ..."
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The wellknown recursive descent parsing method for contextfree grammars is extended for their generalization, Boolean grammars, which include explicit settheoretic operations in the formalism of rules. Conjunction is implemented by scanning a part of the input multiple times, while the mechanism of exception handling is used to implement negation. A subclass of LL(k) Boolean grammars, for which recursive descent parsing is possible, is identified, the construction of a parsing table and parser code is formally specified and illustrated by an example. Correctness of the method is proved.
Generalised LR parsing algorithms
, 2006
"... This thesis concerns the parsing of contextfree grammars. A parser is a tool, defined for a specific grammar, that constructs a syntactic representation of an input string and determines if the string is grammatically correct or not. An algorithm that is capable of parsing any contextfree grammar ..."
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This thesis concerns the parsing of contextfree grammars. A parser is a tool, defined for a specific grammar, that constructs a syntactic representation of an input string and determines if the string is grammatically correct or not. An algorithm that is capable of parsing any contextfree grammar is called a generalised (contextfree) parser. This thesis is devoted to the theoretical analysis of generalised parsing algorithms. We describe, analyse and compare several algorithms that are based on Knuth’s LR parser. This work underpins the design and implementation of the Parser Animation Tool (PAT). We use PAT to evaluate the asymptotic complexity of generalised parsing algorithms and to develop the Binary Right Nulled Generalised LR algorithm – a new cubic worst case parser. We also compare the Right Nullable Generalised LR, Reduction Incorporated Generalised LR, Farshi, Tomita and Earley algorithms using the statistical data collected by PAT. Our study indicates that the overheads associated with some of the parsing algorithms may have significant consequences on their behaviour.