Property Specification Language

Property Specification Language (PSL) is a temporal logic extending linear temporal logic with a range of operators for both ease of expression and enhancement of expressive power. PSL makes an extensive use of regular expressions and syntactic sugaring. It is widely used in the hardware design and verification industry, where formal verification tools (such as model checking) and/or logic simulation tools are used to prove or refute that a given PSL formula holds on a given design.
PSL was initially developed by Accellera for specifying properties or assertions about hardware designs. Since September 2004 the standardization on the language has been done in IEEE 1850 working group. In September 2005, the IEEE 1850 Standard for Property Specification Language (PSL) was announced.
Syntax and semantics.
PSL can express that if some scenario happens now, then another scenario should happen some time later. For instance, the property "a should always eventually be ed" can be expressed by the PSL formula: 
 always (request -> eventually! grant) 
The property "every which is immediately followed by an signal, should be followed by a complete , where a complete data transfer is a sequence starting with signal , ending with signal in which holds at the meantime" can be expressed by the PSL formula: 
 (true[*]; req; ack) |=> (start; busy[*]; end) 
A trace satisfying this formula is given in the figure on the right.
PSL's temporal operators can be roughly classified into "LTL-style" operators and "regular-expression-style" operators. Many PSL operators come in two versions, a strong version, indicated by an exclamation mark suffix ( ), and a weak version. The "strong version" makes eventuality requirements (i.e. require that something will hold in the future), while the "weak version" does not. An "underscore suffix" ( ) is used to differentiate "inclusive" vs. "non-inclusive" requirements. An and suffixes are used to denote "universal" (all) vs. "existential" (exists) requirements. Exact time windows are denoted by and flexible by . 
SERE-style operators.
The most commonly used PSL operator is the "suffix-implication" operator (a.k.a. the "triggers" operator), which is denoted by . Its left operand is a PSL regular expression and its right operand is any PSL formula (be it in LTL style or regular expression style). The semantics of is that on every time point i such that the sequence of time points up to i constitute a match to the regular expression r, the path from i+1 should satisfy the property p. This is exemplified in the figures on the right.
The regular expressions of PSL have the common operators for concatenation (), Kleene-closure (), and union (), as well as operator for fusion (), intersection () and a weaker version (), and many variations for consecutive counting and in-consecutive counting e.g. and .
The trigger operator comes in several variations, shown in the table below.
Here and are PSL-regular expressions, and is a PSL formula.
Operators for concatenation, fusion, union, intersection and their variations are shown in the table below.
Here and are PSL regular expressions.
Operators for consecutive repetitions are shown in the table below.
Here is a PSL regular expression. 
Operators for non-consecutive repetitions are shown in the table below.
Here is any PSL Boolean expression. 
LTL-style operators.
Below is a sample of some LTL-style operators of PSL.
Here and are any PSL formulas.
Sampling operator.
Sometimes it is desirable to change the definition of the "next time-point", for instance in multiply-clocked designs, or when a higher level of abstraction is desired. The "sampling operator" (a.k.a. "the clock operator"), denoted , is used for this purpose. The formula where is a PSL formula and a PSL Boolean expressions holds on a given path if on that path projected on the cycles in which holds, as exemplified in the figures to the right. 
The first property states that "every which is immediately followed by an signal, should be followed by a complete , where a complete data transfer is a sequence starting with signal , ending with signal in which should hold at least 8 times: 
 ((true[*]; req; ack) |=> (start; data[=8]; end) 
But sometimes it is desired to consider only the cases where the above signals occur on a cycle where is high. 
This is depicted in the second figure in which although the formula 
 ((true[*]; req; ack) |=> (start; data[*3]; end) @ clk 
uses and is consecutive repetition, the matching trace has 3 non-consecutive time points where holds, but when considering only the time points where holds, the time points where hold become consecutive. 
The semantics of formulas with nested @ is a little subtle. The interested reader is referred to [2].
Abort operators.
PSL has several operators to deal with truncated paths (finite paths that may correspond to a prefix of the computation). Truncated paths occur in bounded-model checking, due to resets and in many other scenarios. The abort operators, specify how eventualities should be dealt with when a path has been truncated. They rely on the truncated semantics proposed in [1].
Here is any PSL formula and is any PSL Boolean expression. 
Expressive power.
PSL subsumes the temporal logic LTL and extends its expressive power to that of the omega-regular languages. The augmentation in expressive power, compared to that of LTL, which has the expressive power of the star-free ω-regular expressions, can be attributed to the "suffix implication", a.k.a. "triggers" operator, denoted "|->". The formula "r |-> f" where "r" is a regular expression and "f" is a temporal logic formula holds on a computation "w" if any prefix of "w" matching "r" has a continuation satisfying "f". Other non-LTL operators of PSL are the "@" operator, for specifying multiply-clocked designs, the "abort" operators, for dealing with hardware resets, and "local variables" for succinctness.
Layers.
PSL is defined in 4 layers: the "Boolean layer", the "temporal layer", the "modeling layer" and the "verification layer".
Language compatibility.
Property Specification Language can be used with multiple electronic system design languages (HDLs) such as:
When PSL is used in conjunction with one of the above HDLs, its Boolean layer uses the operators of the respective HDL.